What should be the interest rate for an amount to become 5 times of itself at simple interest in 50 years?

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.

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Answer : A

Solution : Let the sum be Rs. X. <br> `therefore "Amount = Rs. 5x` <br> Simple interest = Amount - Principal = Rs. 5x - Rs x = Rs. 4x <br> Let the number of years be n. <br> We have simple interest `=(PTR)/(100)`. <br> `rArr 4x = (x xx n xx 20)/(100)` <br> `rArr 4 = (n)/(5) rArr n= 20` <br> `therefore` In 20 years, the sum becomes 5 times itself. <br> Hence, the correct option is (a).

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A sum of money becomes 8 / 5 of itself in 5 years at a certain rate of simple interest .find the rate of interest.

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Solution

Given: Time, T=5 yearsLet the principal be PRate of interest =R Amount, A=8P5Simple Interest, S.I= Amount − Principal =8P5−P=3P5 ∴S.I=3P5 Again, S.I=P×R×T100⇒3P5=P×R×5100⇒35=5R100⇒35=R20⇒R=3×205⇒R=3×4∴R=12. The required rate of interest is 12%.

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