Question

You have just invested $3,000 into an account that will earn a 9% APR compounded monthly. You want to have exactly $8,000 in the account at the end of 5 years. The account allows you to make one deposit at the end of the first year. In order to have exactly $8,000 at the end of year 5, how much must you deposit at the end of the first year?

Answer 1

We use the formula:
A=P(1+r/1200)^12n
where
A=future value
P=present value
r=rate of interest
n=time period.

8000=3000*(1+0.09/12)^(12*5)+Deposit at end of first year*(1+0.09/12)^(12*4)

8000=3000*1.565681027+Deposit at end of first year*1.431405333

Deposit at end of first year=(8000-4697.043081)/1.431405333

=$2307.49(Approx).