Question

You want to accumulate $5,000 in five years by making a deposit of X today and another deposit of 3X in two years. If the effective rate of interest is 5%. Determine X?

Answer 1

rate of interest = r = 5%

Deposit today = C₀ = X

Deposit in year 2 = C₂ = 3X

year	0	1	2	3	4	5
Deposit	X		3X

Future value of the deposits = FV = $5000

Future value of the deposit C₀ at year 5 = FV₀ = X*(1+5%)⁵ = 1.2762815625*X

Future value of deposit C₂ at year 5 = FV₂ = 3X*(1+5%)³ = 1.157625*3X = 3.472875*X

FV = FV₀ + FV₂ = 1.2762815625*X + 3.472875*X = 4.7491565625*X = 5000

X = 5000/4.7491565625 = 1052.81852349967

Answer -> X = $1052.82 (Rounded to two-decimal places)