Question

Suppose a young couple deposits $700 at the end of each quarter in an account that earns 7.1%, compounded quarterly, for a period of 6 years. After the 6 years, they start a family and find they can contribute only $200 per quarter. If they leave the money from the first 6 years in the account and continue to contribute $200 at the end of each quarter for the next 18½ years, how much will they have in the account (to help with their child's college expenses)?

Answer 1

Part 1:
R=$700 per quarter
i=7.1%/4 per quarter
n=6*4=24 quarters
S=future value
=R((1+i)^n-1)/i
=700((1+.071/4)^24-1)/(.071/4)
=$20,720.40

After 6 years,
S1=future value (after 18.5 years) of initial investment
=S(1+i)^n
=$20720.40(1+.071/4)^74
=$76179.91

R=$200 per quarter
i=7.1%/4 per quarter
n=18.5*4=74 quarters
S2=future value for further contributions
=200((1+.071/4)^74-1)/(.071/4)
=$30,158.48

Total future value
= $76179.91+$30158.48
= $106,338.39

Check the calculations please.