Question

Reaching a Financial Goal You need to accumulate $10,000. To do so, you plan to make deposits of $1,800 per year - with the first payment being made a year from today - into a bank account that pays 11.25% annual interest. Your last deposit will be less than $1,800 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal? Round your answer up to the nearest whole number.

? year(s)

How large will the last deposit be? Round your answer to the nearest cent. ?

Answer 1

The number of years taken to reach goal is calculated using NPER function in Excel ;

rate = 11.25%

pmt = -1800 (Yearly deposit. This is entered with a negative sign because it is a cash outflow)

pv = 0 (amount currently saved is zero)

fv = 10000 (Required ending value of account)

NPER is calculated to be 4.55

A1 x fc =NPER(11.25%,-1800,0,10000) D E F G A B C

This is rounded off to 5.

It will take 5 years to reach your goal

First, we calculate the value of account after 4 deposits using FV function in Excel :

rate = 11.25%

nper = 4

pmt = -1800

FV is calculated to be $8,508.69

А3 х v f =FV(11.25%,4,-1800) B C D E A з | $8,508.69 |

Value of account at end of 5 years (before final deposit) = $8,508.69 * (1 + 11.25%) = $9,465.92

Last deposit = required value of account - value of account at end of 5 years (before final deposit)

Last deposit = $10,000 - $9,465.92

Last deposit = $534.08