Question

Reaching a Financial Goal

You need to accumulate $10,000. To do so, you plan to make deposits of $1,750 per year - with the first payment being made a year from today - into a bank account that pays 7% annual interest. Your last deposit will be less than $1,750 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

	We have the equality, 10000 = 1750*FVIFA(7,n)
	FVIFA(7,n) = 10000/1750 = 5.7143	5.714285714
	From the interest factor tables for 4%, the factor is 4.4399 for n = 4
	and 5.7507 for n = 5.
1]	The goal of $10,000 will be reached in 5 years
	So the full deposits need to be made for 4 years.
	FV at t5 of the deposits for 4 years = 1750*(1.07^4-1)*1.07/(0.07) =	$            8,313.79
2]	Last deposit to be made at t5 = 10000-8313.79 =	$            1,686.21