The Power of Compounding Interest

Quantitative Finance Level 1

If you are 20, and invest $1,000 today in an investment that returns 5% a year, compounding. When you are 70, 50 years later, will your investment be worth more or less than 10 times your initial investment (ignoring inflation)? Will your investment be worth more or less than $10,000?

It will be worth more than 10X It will be worth less than 10X

Christopher Williams by Christopher Williams , 33, USA

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2 solutions

The compounding interest formula (found on Interest Rates ) is A = P ( 1 + R 100 ) t \text{A} = \text{P}{\left(1 + \dfrac{\text{R}}{100}\right)}^{\text{t}}
where A \text{A} is the total amount at the end of the time period, P \text{P} is the principal amount, R \text{R} is the rate of interest, t \text{t} is the number of times the interest compounds in this time period, for annual compounding this is the number of years.

For this problem that means:

A = P ( 1 + R 100 ) t \text{A} = \text{P}{\left(1 + \dfrac{\text{R}}{100}\right)}^{\text{t}}
= 1000 ( 1 + 5 100 ) 50 = 1000{\left(1 + \dfrac{5}{100}\right)}^{50}
= 1000 ( 1.05 ) 50 = 1000{\left(1.05\right)}^{50}
= 1000 ( 1.05 ) 50 = 1000{\left(1.05\right)}^{50}
= $ 11 , 467.40 > $ 10 , 000 = \$ 11,467.40 > \$ 10,000

16 Helpful 2 Interesting 1 Brilliant 2 Confused

Hey , what if u look at it this way..... %% interest per year so $50 per year ...and in 50 years 50*50=$2500 which is less than $10,000

Sanad Kadu - 3 years, 2 months ago

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it is compound interest not simple interest

tausif mirza - 3 years, 2 months ago

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Sorry , but can you help me out this is not my cup of tea but i would surely like to make it mine..........what is the diffrence?

Sanad Kadu - 3 years, 2 months ago

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@Sanad Kadu – With simple interest, the interest would be calculated just on the principal, and you would receive the same interest payment every year. This is what you initially suggested in your answer - a payment of $50 per year. However this problem assumes compounding interest.

Compounding interest means that you earn interest on the principal and the interest earned . So you earn interest at some regular rate and then that interest earns more interest.

For instance, in this problem, at the end of Year One you would have $1,000 plus $50 of interest from the principal = $1,050, then at the end of Year Two you would have your $1,050 from last year, plus that $50 of interest from your initial principal you earn annually, plus last year's fifty dollars earned $2.50 of interest this year. So you have $1,050 + $50 + $2.50 = $1,102.50.

The power of compound investing is that you earn interest on your interest!

Christopher Williams - 3 years, 1 month ago

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@Christopher Williams – Got it Chirs , love Brilliant , Thanks

Sanad Kadu - 3 years, 1 month ago

Sanad, that's not compounding. Is it? you are just finding the interest earned in 1 year for the rest of years as well. That's Simple Interest.

Adarsh Pathak - 1 year, 11 months ago

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Your method ignores the interest on the interest already earned which is the real power (or danger in the case of debt) of compounding.

David Davis - 1 year, 7 months ago

1000(1+0.05)^50=11467.39 Using the compounding interest rate

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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