A 20 year loan with payments at the end of each year involves payments of $1,...

A 20 year loan with payments at the end of each year involves payments of $1, 000 for the first 10 years, and then for the next 10 years payments are 3% larger than the previous year’s payment. If effective annual interest is 5% then find the original loan amount. please dont solve using excel

Expert Solution

P1 = Annual Loan payment = $1,000

P2 = First Annual Loan payment = $1,000 * (1+3%) = $1,030

n = 10 years

g = growth rate = 3%

r = discount rate = 5%

Loan Amount = [P1 * [1 - (1+r)^-n] / r] + [[P2 / (r-g)] * [1 - [(1+g)/(1+r)]^n] / (1+r)^n

= [$1,000 * [1 - (1+5%)^-10] / 5%] + [[$1,030 / (5%-3%)] * [1 - [(1+3%)/(1+5%)]^10] / (1+5%)^10

= [$1,000 * 0.386086746 / 0.05] + [$51,500 *0.174951923] / 1.62889463

= $7,721.73492 + $5531.37316

= $13,253.1081

Therefore, Loan amount is $13,253.11

jeff jeffy answered 2 years ago

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