Question

You need to accumulate $10,000. To do so, you plan to make deposits of $1,100 per year - with the first payment being made a year from today - into a bank account that pays 11.82% annual interest. Your last deposit will be less than $1,100 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.

Answer 1

Step-by-step explanation:

Using future annuity formula

Fv = Pmt ( (1+r)ⁿ -1 )/ r

`(FVr)/(Pmt)` + 1 = (1+r)ⁿ

In (
`(FVr)/(Pmt)` + 1) = n In ( 1+r)

n = In (
`(FVr)/(Pmt)` + 1) / In ( 1 + r)

FV, future value = $10,000, Pmt, periodic payment per year = $1,100, r rate = 11.82% = 0.1182 and n = number of years

n = 0.7297 / 0.11172 = 6.53 years approx 7 years

the last year payment will actually be less than $1,100