What time 8000 will amount to 9261 at 10% per annum compound interest when the interest is compounded half yearly?

We will learn how to use the formula for calculating the compound interest when interest is compounded half-yearly.

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• What is the compounded annual interest for a loan amount of Rs 8000 at 10% per annum for a period of 2 years?
• What is the compound interest on $1000 at 10% per annum for 2 years compounded annually?
• What is the compound interest on Rs 10000 for 2 years at rate of interest 10% per annum?
• What is the compound interest on rupees 20000 at 10% for 2 years?

Computation of compound interest by using growing principal becomes lengthy and complicated when the period is long. If the rate of interest is annual and the interest is compounded half-yearly (i.e., 6 months or, 2 times in a year) then the number of years (n) is doubled (i.e., made 2n) and the rate of annual interest (r) is halved (i.e., made \(\frac{r}{2}\)).  In such cases we use the following formula for compound interest when the interest is calculated half-yearly.

If the principal = P, rate of interest per unit time = \(\frac{r}{2}\)%, number of units of time = 2n, the amount = A and the compound interest = CI

Then

A = P(1 + \(\frac{\frac{r}{2}}{100}\))\(^{2n}\)

Here, the rate percent is divided by 2 and the number of years is multiplied by 2

Therefore,  CI = A - P = P{(1 + \(\frac{\frac{r}{2}}{100}\))\(^{2n}\) - 1}

Note:

A = P(1 + \(\frac{\frac{r}{2}}{100}\))\(^{2n}\) is the relation among the four quantities P, r, n and A.

Given any three of these, the fourth can be found from this formula.

CI = A - P = P{(1 + \(\frac{\frac{r}{2}}{100}\))\(^{2n}\) - 1} is the relation among the four quantities P, r, n and CI.

Given any three of these, the fourth can be found from this formula.

Word problems on compound interest when interest is compounded half-yearly:

1. Find the amount and the compound interest on $ 8,000 at 10 % per annum for 1\(\frac{1}{2}\) years if the interest is compounded half-yearly.

Solution:

Here, the interest is compounded half-yearly. So,

Principal (P) = $ 8,000

Number of years (n) = 1\(\frac{1}{2}\) × 2 = \(\frac{3}{2}\) × 2 = 3

Rate of interest compounded half-yearly (r) = \(\frac{10}{2}\)% = 5%

Now, A = P (1 + \(\frac{r}{100}\))\(^{n}\)

⟹ A = $ 8,000(1 + \(\frac{5}{100}\))\(^{3}\)

⟹ A = $ 8,000(1 + \(\frac{1}{20}\))\(^{3}\)

⟹ A = $ 8,000 × (\(\frac{21}{20}\))\(^{3}\)

⟹ A = $ 8,000 × \(\frac{9261}{8000}\)

⟹ A = $ 9,261 and

Compound interest = Amount - Principal

                          = $ 9,261 - $ 8,000

                          = $ 1,261

Therefore, the amount is $ 9,261 and the compound interest is $ 1,261

2. Find the amount and the compound interest on $ 4,000 is 1\(\frac{1}{2}\) years at 10 % per annum compounded half-yearly.

Solution:

Here, the interest is compounded half-yearly. So,

Principal (P) = $ 4,000

Number of years (n) = 1\(\frac{1}{2}\) × 2 = \(\frac{3}{2}\) × 2 = 3

Rate of interest compounded half-yearly (r) = \(\frac{10}{2}\)% = 5%

Now, A = P (1 + \(\frac{r}{100}\))\(^{n}\)

⟹ A = $ 4,000(1 + \(\frac{5}{100}\))\(^{3}\)

⟹ A = $ 4,000(1 + \(\frac{1}{20}\))\(^{3}\)

⟹ A = $ 4,000 × (\(\frac{21}{20}\))\(^{3}\)

⟹ A = $ 4,000 × \(\frac{9261}{8000}\)

⟹ A = $ 4,630.50 and

Compound interest = Amount - Principal

                          = $ 4,630.50 - $ 4,000

                          = $ 630.50

Therefore, the amount is $ 4,630.50 and the compound interest is $ 630.50

● Compound Interest

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Problems on Compound Interest

Variable Rate of Compound Interest

Practice Test on Compound Interest

● Compound Interest - Worksheet

Worksheet on Compound Interest

Worksheet on Compound Interest with Growing Principal

Worksheet on Compound Interest with Periodic Deductions

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What is the compounded annual interest for a loan amount of Rs 8000 at 10% per annum for a period of 2 years?

8000Period (n) = 2 yearsRate (R1)=9% for the first yearR2=10% the second year∴ Amount (A)= P (1+R1100)1(1+R2100)1=8000 (1+9100) (1+10100)=Rs. 8000×109100×110100=Rs. 9592. Q.

What is the compound interest on $1000 at 10% per annum for 2 years compounded annually?

compound interest after 2yrs of 1000 Rs at the rate 10% per annum is 210 Rs. it is given that principal , P = 1000 Rs. = 210 Rs. ∴Hence, compound interest = 210 Rs.

What is the compound interest on Rs 10000 for 2 years at rate of interest 10% per annum?

Compound Interest would be 12100rs.

What is the compound interest on rupees 20000 at 10% for 2 years?

Where P is principal, R is rate of interest and T is time. ∴ The compound interest for 2 years is Rs. 2464.

In what time ₹ 8000 will amount to ₹ 9261 at 10% compound interest per annum interest being compounded half yearly?

In what time will Rs 8000 amount to Rs 9261 at 5% pa when compounded annually?

At what rate percent per annum will sum of Rs 8000 amount to Rs 9261 in 3 years compounded annually?

At what rate of interest per annum will a sum of 8000?