Question

A person deposits money into a retirement account, which pays 7% interest compounded continuously, at a rate of $1000 per year for 20 years. Calculate:

a. The balance of the account at the end of 20 years

b. the amount of money actually deposited into the account

c. the interest earned during the 20 years.

I think i know that for part a you use the integral to find the future value maybe, but i have no idea how to do b or c

Answer 1

compound interest formula is:

FV=PV(1+(r/n))^(nT)

As n approaches infinity, this formula becomes:

FV=PV*e^(rt)

for the 1st $1000 invested:
FV=1000*e^(.07*20)

for the 2nd $1000 invested:
FV=1000*e^(.07*19)

and so on for 20 years. The sum total of future values minus $20,000 deposited is the interest earned in the 20 years.

Answer 2

a.) $43,645.71

b.) just do 1000*20 =20,000

c.) a-b (43,645.71-20,000=23645.71)