Question

Suppose you want to purchase a home for $375,000 with a 30-year mortgage at 5.14% interest. Suppose also that you can put down 25%. What are the monthly payments? (Round your answer to the nearest cent.)

What is the total amount paid for principal and interest? (Round your answer to the nearest cent.)

What is the amount saved if this home is financed for 15 years instead of for 30 years? (Round your answer to the nearest cent.) $

Answer 1

The formula used to calculate the fixed monthly payment (P) required to fully amortize a loan of $ L over a term of n periods at an interest rate of r per period is P = L[r(1 + r)ⁿ]/[(1 + r)ⁿ - 1].

Here L = $ 375,000 – 30 % of $ 375,000 = $ 262500, r = 5.14 % = 5.14/100 = 0.0514 and n = 30 so that P = 262500*0.0514 [(1+0.0514)³⁰]/ [(1+0.0514)³⁰ -1] = 262500*0.0514*4.498204342/3.498204342= $ 17349.48 ( on rounding off to the nearest cent). Thus, the loan of $ 262500 would be fully paid off, with interest , by 30 annual instalments of $ 17349.48 each. Therefore, the amount of interest paid in 30 years is 30*$ 17349.48-$ 262500 = $ ( 520484.40-262599) = $ 257984.40.

If the loan of $ 262500 is paid off in 15 years, then P = 262500*0.0514*(1.0514)¹⁵/[(1.0514¹⁵ -1] = 262500*0.0514*2.120897061/1.120897061= $ 25529.73 ( on rounding off to the nearest cent).

Thus, the loan of $ 262500 would be fully paid off, with interest , by 15 annual instalments of $ 25529.73 each. Therefore, the amount of interest paid in 15 years is 30*$ 25529.73-$ 262500 = $ (382945.95-262500) = $ 120445.95.

Hence, the saving in interest if the condominium were financed for 15 rather than 30 years is $257984.40 -$ 120445.95= $137538.45.