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You want to accumulate $5,000 in five years by making a deposit of X today and...

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?

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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)

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