Question

You would like to have $41,000 in 15 years. To accumulate this​ amount, you plan to deposit each year an equal sum in the​ bank, which will earn 7 percent interest compounded annually. Your first payment will be made at the end of the year.

At the end of 4 years you will receive $9,000 and deposit this in the bank toward your goal of $41,000 at the end of 15 years. In addition to this​ deposit, how much must you deposit in equal annual deposits to reach your​ goal? (Again assume you can earn 7 percent on this​ deposit.)

Answer 1

Sol:

Future value (FV) = $41,000

Period (NPER)= 15 years - 4 years = 11 years

Interest rate = 7%

Amount deposited (PV) = $9000

FV of amount deposited = PV x (1 + r)^n

FV of amount deposited = 9000 x (1 + 7%)^11

FV of amount deposited = 9000 x (1.07)^11

FV of amount deposited = $18,943.67

FV difference between required amount and FV of amount deposited = $41,000 - $18,943.67 = $22,056.33

Amount to be deposit as equal annual deposits to reach the goal we can use PMT function in excel sheet:

FV	22,056.33
NPER	11
Rate	7%
PMT	$1,397.42

Therefore amount to be deposit as equal annual deposits to reach the goal will be $1,397.42

Working