Question

# A loan is repaid with monthly payments for five years, the payments beginning exactly one year...

A loan is repaid with monthly payments for five years, the payments beginning exactly one year after the loan is made. The payments are each \$1,000 in the monthly payments. If the interest rate on the loan is a nominal rate of 6% convertible monthly find the amount of principal in the 42nd paymen

Calculation of Remaining Loan after 41 monthly payments

P = Installment amount = \$1,000

n = 5*12 = 60 months

x = 41

r =interest rate per month = 6%/12 = 0.5%

Loan Balance at the end iof 41 monthly payments = P[1 - (1+r)^-(n-x)] / r

= \$1,000 [1 - (1+0.5%)^-(60-41)] / 0.5%

= \$1,000 * 0.090411781 / 0.005

= \$18,082.36

42nd Installment paid = \$1,000

Interest paid for 42nd installment = \$18,082.36*0.5% = \$9.04

Principal paid = Installment paid - Interest paid

= \$1,000 - \$9.04

= \$990.96

Therefore, Principal paid in 42nd installment is \$990.96

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