Question

The debt is amortized by equal payments made at the end of each payment interval. Compute​ (a) the size of the periodic​ payments; (b) the outstanding principal at the time​ indicated; (c) the interest paid by the payment following the time indicated for finding the outstanding​ principal; and​ (d) the principal repaid by the same payment as in part c.

Debt Principal	Repayment Period	Payment Interval	Interest Rate	Conversion Period	Outstanding Principal​ After:
​$12,000.00	7 years	1 month	9​%	quarterly	7th payment

Answer 1

Given, payment interval= Monthly.

Annual interest rate of 9% compounded quarterly is equivalent to 8.933331% compounded monthly, as follows:

A С Given Given 9.0% Quarterly 4 9.3083% ((1+C2/C4)^C4)-1 1 2 Yearly Nominal Rate (R) 3 Compounding frequency 4 Times compounded a year (t) 5 EAR=((1+R/t)^t)-1 6 7 Frequency 8 Times compounded a year (t) 9 Monthly rate 10 Yearly rate (Monthly compounding) Monthly 12 0.744444% 8.933331% ((1+C5)^1/C8)-1 C9*C8

Part (a): Monthly payment= $192.66

Part (b): Outstanding principal after 7^th payment= $11,260.34

Part (c ):   Time indicated for finding the outstanding principal is 7^th payment. The payment following this time indicated is 8^th payment.

Interest paid by the 8^th payment= $83.33

Part (d): Principal repaid in 8^th payment (the payment indicated in part (c)= $108.84

Details of calculation as below:

D10 Le =PMT(D4,D6,D7,D8,09)*-1 A С D Amounts in $ 1 2 Formula 3 Annual Interest rate (APR) As above 4 Monthly rate APR/12 5 Number of years (N) Given 6 Number of payments N*12 7 Loan amount 220000-20000 8 Future value 9 Timing of payment End of month 10 Monthly payment PMT(D4,D6,D7,08,09)*-1 11 12 After 7 payments: 13 Number of remaining months 84-7 Principal outstanding (PV of 14 future installments) PV(D4,D13,D10,0,0)*-1 15 16 Interest for 8th month CUMIPMT(D4,D6,D7,1,12,0)*-1 17 Principal for 8th month Monthly payment- Interest Function arguments Value 8.933331% Rate 0.74444% 7 Nper 84 PV $12,000 Fv 0 Type 0 PMT $192.66 Nper 77 PV $11,260.34 $ 83.83 $108.84