Given
Principal (P) = Rs 2000
Amount (A) = Rs 2315.25
Period (n) = 3 years
Let the rate of interest be r% p.a.
WKT
A / P = {1 + (r / 100)}n
2315.25 / 2000 = {1 + (r / 100)}3
{1 + (r / 100)}3 = (231525) / (100 × 2000)
On calculating, we get,
\{1+(\mathrm{r} / 100)\}^{3} = 9261 / 8000
\{1+(\mathrm{r} / 100)\}^{3} = (21 / 20)3
We get,
1 + (r / 100) = 21 / 20
r / 100 = (21 / 20) – 1
r / 100 = 1 / 20
We get,
r = 100 / 20
r = 5
Therefore, rate of interest = 5% p.a.
Find the rate percent per annum, if Rs 2000 amount to Rs 2315.25 in an year and a half, interest being compounded six monthly.
Let the rate percent per annum be R.
Because interest is compounded every six months, n will be 3 for 1.5 years.
Now,
\[A = P \left( 1 + \frac{R}{200} \right)^n \]
\[2, 315 . 25 = 2, 000 \left( 1 + \frac{R}{200} \right)^3 \]
\[ \left( 1 + \frac{R}{200} \right)^3 = \frac{2, 315 . 25}{2, 000}\]
\[
\left( 1 + \frac{R}{200} \right)^3 = 1 . 157625\]
\[ \left( 1 + \frac{R}{200} \right)^3 = \left( 1 . 05 \right)^3 \]
\[1 + \frac{R}{200} = 1 . 05\]
\[\frac{R}{200} = 0 . 05\]
\[ = 10\]
Thus, the required rate is 10 % per annum.
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Nội dung chính Show
- 1. The simple interest on a sum of money for 3 years at 6²/₃ % per annum is $ 6750. What will be the compound interest on the same sum at the same rate for the same period, compounded annually?
- 2. The difference between the compound interest, compounded annually and the simple interest on a certain sum for 2 years at 6% per annum is $ 18. Find the sum.
- 3. A certain sum amounts to $ 72900 in 2 years at 8% per annum compound interest, compounded annually. Find the sum.
- 4. In this question the formula is when the interest is compounded annually to solve this problem on compound interest. 4. At what rate per cent per annum will Ron lends a sum of $2000 to Ben. Ben returned after 2 years $2205, compounded annually?
- 5. A man deposited $1000 in a bank. In return he got $1331. Bank gave interest 10% per annum. How long did he kept the money in the bank?
- At what rate per annum will Rs 2000 becomes Rs 2205 in 2 years compounded annually?
- At what rate percent per annum will a sum of PHP 2000 amount to PHP 2205 in 2 years compounded annually?
- At what rate percent per annum will a sum of rupees 2000 amount to rupees?
- At what rate percent of compound interest will 625 become 784 in 2 years?
- At what rate percent per annum will a sum of ₹ 2000 amount to ₹ 2205 in 2 years compounded annually?
- At what rate percent per annum of compound interest will Rs 2000 amounts to Rs 2332.8 in 2 years?
- At what rate percent per annum will a sum of Rs 2000 amount to?
- In what time will Rs 2000 amounts to Rs 2315.25 at 5% per annum compounded annually?
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Given:
Compound interest on Rs.2000 for 3 years = Rs.315.25
Formulas used:
Amount = Principal + Interest
Amount = P(1 + r/100)n
Calculation:
Amount = 2000 + 315.25 = Rs.2315.25
Amount = P(1 + r/100)n
⇒ 2315.25 = 2000(1 + r/100)3
⇒ 231525/200000 = (1 + r/100)3
⇒ ∛9261/8000 = 1 + r/100
⇒ 21/20 - 1 = r/100
⇒ (21 - 20)/20 = r/100
⇒ 1/20 = r/100
⇒ 1 = r/5
⇒ r = 5
∴ The rate of interest is 5% per annum.
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Find the rate percent per annum, if Rs 2000 amount to Rs 2315.25 in an year and a half, interest being compounded six monthly.
Let the rate percent per annum be R.
Because interest is compounded every six months, n will be 3 for 1.5 years.
Now,
\[A = P \left( 1 + \frac{R}{200} \right)^n \]
\[2, 315 . 25 = 2, 000 \left( 1 + \frac{R}{200} \right)^3 \]
\[ \left( 1 + \frac{R}{200} \right)^3 = \frac{2, 315 . 25}{2, 000}\]
\[ \left( 1 + \frac{R}{200} \right)^3 = 1 . 157625\]
\[ \left( 1 + \frac{R}{200} \right)^3 = \left( 1 .
05 \right)^3 \]
\[1 + \frac{R}{200} = 1 . 05\]
\[\frac{R}{200} = 0 . 05\]
\[ = 10\]
Thus, the required rate is 10 % per annum.
Solution : Given:<br>Principle `(P)=Rs.2000`<br>Amount `(A)=Rs.2315.25`<br>`n=1.5` years means `3` half-years.<br>The rate has to be calculated half-yearly, therefore let `R` be the rate of half-yearly.<br>As we know that,<br>`A=P(1+R/100)^n`<br>`therefore 2315.25=2000(1+R/100)^3`<br>`2315.25/2000=(1+R/100)^3`<br>`231525/2000times100=(1+R/100)^3`<br>`9261/8000=(1+R/100)^3`<br>`(21/20)^3=(1+R/100)^3`<br>`21/20=1+R/100`<br>`21/20-1=R/100`<br>`(21-20)/20=R/100`<br>`1/20=R/100`<br>`R=100/20`<br>`R=5%`.<br>Hence, the rate will be `5%` half yearly and `10%` yearly.
Nội dung chính Show
- 1. The simple interest on a sum of money for 3 years at 6²/₃ % per annum is $ 6750. What will be the compound interest on the same sum at the same rate for the same period, compounded annually?
- 2. The difference between the compound interest, compounded annually and the simple interest on a certain sum for 2 years at 6% per annum is $ 18. Find the sum.
- 3. A certain sum amounts to $ 72900 in 2 years at 8% per annum compound interest, compounded annually. Find the sum.
- 4. In this question the formula is when the interest is compounded annually to solve this problem on compound interest. 4. At what rate per cent per annum will Ron lends a sum of $2000 to Ben. Ben returned after 2 years $2205, compounded annually?
- 5. A man deposited $1000 in a bank. In return he got $1331. Bank gave interest 10% per annum. How long did he kept the money in the bank?
- At what rate per annum will Rs 2000 becomes Rs 2205 in 2 years compounded annually?
- At what rate percent per annum will a sum of PHP 2000 amount to PHP 2205 in 2 years compounded annually?
- At what rate percent per annum will a sum of rupees 2000 amount to rupees?
- At what rate percent of compound interest will 625 become 784 in 2 years?
More solved problems on compound interest using formula are shown below.
1. The simple interest on a sum of money for 3 years at 6²/₃ % per annum is $ 6750. What will be the compound interest on the same sum at the same rate for the same period, compounded annually?
Solution:
Given, SI = $ 6750, R = \(\frac{20}{3}\)% p.a. and T = 3 years.
sum = 100 × SI / R × T
= $ (100 × 6750 × ³/₂₀ × 1/3 ) = $ 33750.
Now, P = $ 33750, R = \(\frac{20}{3}\)% p.a. and T = 3 years.
Therefore, amount after 3 years
= $ {33750 × (1 + (20/3 × 100)}³ [using A = P (1 + R/100)ᵀ]
= $ (33750 × 16/15 × 16/15 × 16/15) = $ 40960.
Thus, amount = $ 40960.
Hence, compound interest = $ (40960 - 33750) = $ 7210.
2. The difference between the compound interest, compounded annually and the simple interest on a certain sum for 2 years at 6% per annum is $ 18. Find the sum.
Solution:
Let the sum be $ 100. Then,
SI = $ (100 × 6 × 2/100) = $ 12
and compound interest = $ {100 × (1 + 6/100)² - 100}
= $ {(100 × 53/50 × 53/50) - 100} = $ (2809/25 - 100) = $ 309/25
Therefore, (CI) - (SI) = $ (309/25 – 100) = $ 9/25
If the difference between the CI and SI is $ 9/25, then the sum = $ 100.
If the difference between the CI and SI is $ 18, then the sum = $ (100 × 25/9 × 18 )
= $ 5000.
Hence, the required sum is $ 5000.
Alternative method
Let the sum be $ P.
Then, SI = $ (P × 6/100 × 2) = $ 3P/25
And, CI = $ {P × (1 + 6/100)² - P}
= $ {(P × 53/50 × 53/50) - P} = $ (\(\frac{2809}{2500}\)P - P) = $ (309P/2500)
(CI) - (SI) = $ (309P/2500 – 3P/25) = $ (9P/2500)
Therefore, 9P/2500 = 18
⇔ P = 2500 × 18/9
⇔ P = 5000.
Hence, the required sum is $ 5000.
3. A certain sum amounts to $ 72900 in 2 years at 8% per annum compound interest, compounded annually. Find the sum.
Solution:
Let the sum be $ 100. Then,
amount = $ {100 × (1 + 8/100)²}
= $ (100 × 27/25 × 27/25) = $ (2916/25)
If the amount is $ 2916/25 then the sum = $ 100.
If the amount is $ 72900 then the sum = $ (100 × 25/2916 × 72900) = $ 62500.
Hence, the required sum is $ 62500.
Alternative method
Let the sum be $ P. Then,
amount = $ {P × (1 + 8/100)²}
= $ {P × 27/25 × 27/25} = $ (729P/625)
Therefore, 729P/625 = 72900
⇔ P = (72900 × 625)/729
⇔ P = 62500.
Hence, the required sum is $ 62500.
4. In this question the formula is when the interest is compounded annually to solve this problem on compound interest. 4. At what rate per cent per annum will Ron lends a sum of $2000 to Ben. Ben returned after 2 years $2205, compounded annually?
Solution:
Let the required rate be R% per annum.
Here, A = $ 2205, P = $ 2000 and n = 2 years.
Using the formula A = P(1 + R/100)ⁿ,
2205 = 2000 × ( 1 + R/100)²
⇒ (1 + R/100)² = 2205/2000 = 441/400 = (21/20)²
⇒ ( 1 + R/100) = 21/20
⇒ R/100 = (21/20 – 1) = 1/20
⇒ R = (100 × 1/20) = 5
Hence, the required rate of interest is 5% per annum.
5. A man deposited $1000 in a bank. In return he got $1331. Bank gave interest 10% per annum. How long did he kept the money in the bank?
Solution:
Let the required time be n years. Then,
amount = $ {1000 × (1 + 10/100)ⁿ}
= $ {1000 × (11/10)ⁿ}
Therefore, 1000 × (11/10)ⁿ = 1331 [since, amount = $ 1331 (given)]
⇒ (11/10)ⁿ = 1331/1000 = 11 × 11 × 11/ 10 × 10 × 10 = (11/10)³
⇒ (11/10)ⁿ = (11/10)³
⇒ n = 3.
Thus, n = 3.
Hence, the required time is 3 years.
● Compound Interest
Compound Interest
Compound Interest with Growing Principal
Compound Interest with Periodic
Deductions
Compound Interest by Using Formula
Compound Interest when Interest is Compounded Yearly
Compound Interest when Interest is Compounded Half-Yearly
Compound Interest when Interest is Compounded Quarterly
Problems on Compound Interest
Variable Rate of Compound Interest
Difference of Compound Interest
and Simple Interest
Practice Test on Compound Interest
Uniform Rate of Growth
Uniform Rate of Depreciation
Uniform Rate of Growth and Depreciation
● Compound Interest - Worksheet
Worksheet on Compound Interest
Worksheet on Compound Interest when Interest is Compounded
Half-Yearly
Worksheet on Compound Interest with Growing Principal
Worksheet on Compound Interest with Periodic Deductions
Worksheet on Variable Rate of Compound Interest
Worksheet on Difference of Compound Interest and Simple Interest
Worksheet on Uniform Rate of Growth
Worksheet on Uniform Rate of Depreciation
Worksheet
on Uniform Rate of Growth and Depreciation
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At what rate per annum will Rs 2000 becomes Rs 2205 in 2 years compounded annually?
∴ Rate =5% half yearly or 10% p.a. Q. A sum amounts to Rs. 756.25 at 10% per annum in 2 years, compounded annually.
At what rate percent per annum will a sum of PHP 2000 amount to PHP 2205 in 2 years compounded annually?
⟹r=0. 05=5%
At what rate percent per annum will a sum of rupees 2000 amount to rupees?
Hence, the rate of interest will be equal to 5%.
At what rate percent of compound interest will 625 become 784 in 2 years?
∴R=100×325=4×3=12%
At what rate percent per annum will a sum of ₹ 2000 amount to ₹ 2205 in 2 years compounded annually?
Hence, the required rate of interest is 5%. Was this answer helpful?
At what rate percent per annum of compound interest will Rs 2000 amounts to Rs 2332.8 in 2 years?
This is Expert Verified Answer Given, Principal = 2000, A = 2332.80, Time n = 2 years. ⇒ r = 8. Therefore, R = 8%.
At what rate percent per annum will a sum of Rs 2000 amount to?
Hence, the rate of interest will be equal to 5%.
In what time will Rs 2000 amounts to Rs 2315.25 at 5% per annum compounded annually?
Given A = 2000, P = 2315.25, n = 3 years. r = 5%. Therefore the required rate is 5% per annum.