Determine the periodic deposit. Round up to the nearest dollar. How much of the financial goal comes from deposits and how much comes from interest?

Question

Periodic Deposit: $? at the end of every three months

Rate: 8.25% compounded quarterly

Time: 40 years

Financial Goal: $1,000,000

Answer 1

The Future value is $1,000,000. discounted back to present value over 160 quarters (40 years at 8.25% we get PV = 38,142.36. Let A = the amount of each deposit.

PV = (A/i)(1 - (1/(1+i))^160). so i*PV = A(1-(1/(1+.0825/4))^160. = (.0825/4)*PV

so .(0825/4)*38142.36 = A*(.96185). so divide both sides by .96185 and get A = 786.68 as a monthly deposit. A total of 160 deposits of $786.78 gives a total of $125,869.78 in deposits the balance of the $1,000,000 will come from interest or 874.130.21