On what sum of money will the simple interest and compound interest for 2years at 5% per annum be equal to Rs 50?

The sooner you start to save, the more you'll earn with compound interest.

How compound interest works

Compound interest is the interest you get on:

• the money you initially deposited, called the principal
• the interest you've already earned

For example, if you have a savings account, you'll earn interest on your initial savings and on the interest you've already earned. You get interest on your interest.

This is different to simple interest. Simple interest is paid only on the principal at the end of the period. A term deposit usually earns simple interest.

Save more with compound interest

The power of compounding helps you to save more money. The longer you save, the more interest you earn. So start as soon as you can and save regularly. You'll earn a lot more than if you try to catch up later.

For example, if you put $10,000 into a savings account with 3% interest compounded monthly:

• After five years, you'd have $11,616. You'd earn $1,616 in interest.
• After 10 years you'd have $13,494. You'd earn $3,494 in interest.
• After 20 years you'd have $18,208. You'd earn $8,208 in interest.

Compound interest formula

To calculate compound interest, use the formula:

A = P x (1 + r)n

A = ending balance
P = starting balance (or principal)
r = interest rate per period as a decimal (for example, 2% becomes 0.02)
n = the number of time periods

How to calculate compound interest

To calculate how much $2,000 will earn over two years at an interest rate of 5% per year, compounded monthly:

1. Divide the annual interest rate of 5% by 12 (as interest compounds monthly) = 0.0042

2. Calculate the number of time periods (n) in months you'll be earning interest for (2 years x 12 months per year) = 24

3. Use the compound interest formula

A = $2,000 x (1+ 0.0042)24
A = $2,000 x 1.106
A = $2,211.64

Lorenzo and Sophia compare the compounding effect

Lorenzo and Sophia both decide to invest $10,000 at a 5% interest rate for five years. Sophia earns interest monthly, and Lorenzo earns interest at the end of the five-year term.

After five years:

• Sophia has $12,834.
• Lorenzo has $12,500.

Sophia and Lorenzo both started with the same amount. But Sophia gets $334 more interest than Lorenzo because of the compounding effect. Because Sophia is paid interest each month, the following month she earns interest on interest.

Question

On what sum of money will the difference between the compound interest and simple interest for 2years be equal to Rs 25 if the rate of interest charged for both is 5% p.a. 

Hint:

Use the formula of compound interest and simple interest to get the principal amount.

The correct answer is: Rs 10000

Complete step by step solution:Let the principal amount = PIt is given that the rate of interest R = 5% and number of years T = 2 years.So, compound interest for 2 years = Simple  interest for 2 years = It is given that compound interest - simple interest = 25 RupeesThat is,  Rupees.Hence the principal amount = Rs 10000

On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5% p.a.?

Solution

C.I = `P[(1 + r/100)^2 - 1] = P[(1 + 5/100)^2 - 1] = "41P"/400`

`S.I = (P xx 5 xx 2)/100 = P/100`

Given, C.I. - S.I. Rs. 25

`=> "41P"/400 - P/10 = 25`

`=> (41P - 40P)/400 = 25`

`=> P = 10000`

∴ Required sum  = Rs. 10,000

Concept: Concept of Compound Interest - Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

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The compound interest on a sum of money at 5% per annum for a period of 2 years is ₹ 6560. What will be the simple interest on the same sum for the same period at the same rate?

1. ₹ 6400 
2. ₹ 6440
3. ₹ 6260 
4. ₹ 6380

Answer (Detailed Solution Below)

Option 1 : ₹ 6400 

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Given:

Time = 2 years

Rate, R = 5% per annum

CI = ₹ 6560

Concept:

• \(CI= P[(1+\frac{R}{100})^n-1]\)

• SI = (PRT)/100

Calculation:

We know that,

\(CI= P[(1+\frac{R}{100})^n-1]\)

\(⇒ 6560= P[(1 + \frac{5}{100})^2-1]\)

⇒ 6560 = P[(21/20)2 - 1]

⇒ 6560 = P[(441/400) - 1] 

⇒ 6560 = P(41/400)

⇒ P = 64000

Now, SI = (64000 × 5 × 2)/100

⇒ SI = 6400

Hence, the simple interest is ₹ 6400.

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Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!

Is the simple interest on a sum of money for 2 years at 5% per annum is rupees 50 What is the compound interest on the same sum at the same rate and for the same time?

On what sum of money will CI for 2 years at 5% pa amount to Rs 164?

On what sum of money will the simple interest and compound interest for 2 years at 5% per annum be equal to Rs 63?

On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to rupees 25?