Janelle receives a home improvement loan of $14,508.97 the loan has a nominal in

Question

Janelle receives a home improvement loan of $14,508.97 the loan has a nominal interest rate convertible monthly of 4.8%. The term of the loan is two years and Janelle is expected to make level end-of-month payments, except that she is allowed to miss one payment so long as she then pays higher-level payments for the remainder of the two years, so as to have repaid the loan at the end of the two-year period. Suppose Janelle misses the payment at the end of the ninth month. What must her new level payments be? The answer is $678.95. Please show steps. Thanks!

Explanation / Answer

Given,

Payment = PVr/(1-(1+r)&-n)

4.8 converted monthly will give us r = 4.8/12 = .4

= 14,508.97*.004/(1-1.004^-24) = 635.23

for loan outstanding at the end of 9 months,

payments have already been made for 8 months,

cash flow is calculated at end of 9 months,

so we need to use a 1.004 multiplier for normal FV formula 14,508.97*1.004^9 - 635.23*1.004(1.004^8-1)/.004 = 9865.56

Payment to be made over remaining 15 months 9865.56*.004/(1-1.004^-15) = 678.95

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