Question

A payment of $2,550 is due in 2 years and $3,300 is due in 4 years....

A payment of $2,550 is due in 2 years and $3,300 is due in 4 years. These two original payments are to be rescheduled with a payment of $2,050 in 1 year and the balance in 3 years. Calculate the payment required in 3 years for the rescheduled option.
Assume that money earns 4.5% compounded semi-annually.

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Answer #1

Effective annual rate, r = (1 + 0.045/2)^2 - 1

r = 0.04550625

First, let's find the value of the original payments at year 3

$2,550 due in year 2 is moved forward by 1 year and $3,300 due in 4 years is discounted back by 1 year

V3 = 2,550 * (1 + 0.04550625)^1 + 3,300/(1 + 0.04550625)^1

V3 = 2,666.0409375 + 3,156.3656362647

V3 = $5,822.4065737647

Now, let's find the value of the resceduled payment of $2,050 in 1 year as of year 3

RV3 = 2,050 * (1 + 0.04550625)^2

RV3 = $2,240.8208035176

The balance in year 3 = V3 - RV3

The balance in year 3 = 5,822.4065737647 - 2,240.8208035176

The balance in year 3 = $3,581.5857702471

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