Question

Loan payments of $4000 due 200 days ago and $6000 due 63 days ago are to be replaced
by a payment of$5000 today and the balance 92 days from today. If money is worth 8.3%
and the agreed focal date is 92 days from today, what is the size of the final payment?

Answer 1

The size of the final payment is $5378.08

What is the size of the final payment?

P1 = One loan payment = $4000

P2 = Second loan payment = $6000

P3 = Payment = $5000

Let P4 = Second payment

n1 = 200 days

n2 = 63 days

n3 = 92 days

r = Interest rate = 8.3%

[P1 * (1+ (r * n1 /365))] + [P2 * (1+ (r * n2 /365))] = P3 + [P4 / (1+(r*n3/365)]

[$4000 * (1+(8.3%*200/365)] + [$6000 * (1+(8.3%*63/365)] = $5000 + [P4 / (1+(8.3%*92/365))]

[$4000 * 1.04547945] + [$6000 * 1.01432603] = $5000 + [P4 / 1.02092055]

$4181.9178 + $6085.95618 = $5000 + [P4/1.02092055]

P4/1.02092055 = $5267.87398

P4 = $5378.080801

Therefore, the size of the final payment is $5378.08

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