Question

Answer fast:How much longer will it take to double your money at 3% simple interest, compared to 3% compound interest? Show all work

Answer 1

It will take 9.33 years longer with simple interest than compound interest.

Explanation:

Let the amount for investment be $1000.

Formula for simple interest :

A = P( 1+ rt )

A = 1000( 1 + 0.03 × 1 )

A = 1000 ( 1.03) = 1030

In one year the interest will be $30.00 for $1,000.

To double your money it will take years = 1000 ÷ 30 = 33.33 years

To calculate how much time it will take to double your money at 3% compound interest, we will use rule of 72.

Formula for Rule of 72 =
`(72)/(R)`

So we put the values :
`(72)/(3)` = 24 years

It will take 24 years with 3% of compound interest and 33.33 years with 3% of simple interest.

24 - 33.33 = 9.33 years longer with simple interest.

Answer 2

For simple interest, the account value is
A = P + I
A = P + Prt
2P = P + P*.03*t . . . . . . we want to double our money
1 = .03*t . . . . . . . . . . . . divide by P, subtract 1
1/.03 = t ≈ 33.3 . . . . years

For interest compounded annually, the account value is
A = P*(1+r)^t
2P =P*1.03^t . . . . . . we want to double our money
2 = 1.03^t . . . . . . . . .divide by P
log(2) = t*log(1.03) . . take logarithms
log(2)/log(1.03) = t ≈ 23.4 . . . . years

It will take about 9.9 years longer to double your money at 3% simple interest compared to 3% interest compounded annually.