Question

Question 60 x Your answer is incorrect. Try again. Shirley would like to borrow $51,500 to pay one year's tuition at a private U.S. university. She would like to make quarterly payments and finish repaying the loan in 6 years. If the bank is quoting her a rate of 7 percent compounded monthly. Determine her quarterly payment. (Round effective interest rate to 4 decimal places, e.g. 25.1253% and final answer to 2 decimal places, e.g. 125.12.) Quarterly payment

Answer 1

Annual interest rate of 7% compounded monthly is equivalent to 7.0409% compounded quarterly, as follows:

Quarterly payment of the loan= $ 2,649.47 as follows:

Сл A B С E F G 1 Quarterly Payments (Payments at the end of each period) 2 Equated Quarterly payment is calculated using the formula EQI=[P*r*(1+r)^n]/[(1+r)^n]-1 3 Where P= Principal (loan amount), n= Number of installments. 4. r=Rate of interest per quarter in decimals. All amounts in $ 6 Given that 7 Principal (loan amount) (P)= 51,500 No. of years (N)= 6 8 Rate of interest % p.a)=R= 7.0409 No. of quarters (n)= 24 9 Calculations: Formula Cell reference Value 11 Interest rate per quarter in decimals (r )=R/(100*4) D8/(100*4) 0.01760225 12 No. of quarter (n)= N*4 G7*4 (1+r)= 1+G11 1.01760225 14 (1+r)^n= G134G8 1.52010436 [(1+r)^n)-1= G14-1 0.52010436 P*r*(1+r)^n= D7*G11*G14 1377.99874 17 Quarterly Payments [P*r*(1+r)^n]/[(1+r)^n]-1 G16/G15 2649.46583 18 Rounded to $ 2,649.47 10 24 13 15 16