One lender offers two mortgages, a 15-year mortgage at 16%, and a 19-year mortgage at 6%.For each, find the total of the monthly payments to repay $135,800.Round to the nearest cent.
A) 15-year: $\$ 341,058.75,19$-year: $\$ 227,908.96$
B) 15-year: $\$ 358,965.87$, 19-year: $\$ 228,237.59$
C) 15-year: $\$ 358,997.21$, 19-year: \$228,032.65
D) 15-year: $\$ 358,988.33$, 19-year: $\$ 229,117.96$
E) $\quad 15$-year: $\$ 359,009.21,19$-year: \$227,908.96

Question

One lender offers two mortgages, a 15-year mortgage at 16%, and a 19-year mortgage at 6%.For each, find the total of the monthly payments to repay $135,800.Round to the nearest cent. 
A) 15-year: $\$ 341,058.75,19$-year: $\$ 227,908.96$
B) 15-year: $\$ 358,965.87$, 19-year: $\$ 228,237.59$
C) 15-year: $\$ 358,997.21$, 19-year: \$228,032.65
D) 15-year: $\$ 358,988.33$, 19-year: $\$ 229,117.96$
E) $\quad 15$-year: $\$ 359,009.21,19$-year: \$227,908.96

Quizplus · Accepted Answer

For the 15-year mortgage at 16%, we have: 
Monthly interest rate = 16%/12 = 1.33%
Total number of payments = 15 x 12 = 180
Using the formula for monthly payment on a mortgage: 
Monthly payment = P * r * (1 + r)^n / [(1 + r)^n - 1]
where P is the principal (loan amount), r is the monthly interest rate, and n is the total number of payments. 
Plugging in the values, we get: 
Monthly payment = 135800 * 0.0133 * (1 + 0.0133)^180 / [(1 + 0.0133)^180 - 1] = $3,331.61
Total of monthly payments = 3,331.61 x 180 = $599,089.80 (rounded to the nearest cent)

For the 19-year mortgage at 6%, we have: 
Monthly interest rate = 6%/12 = 0.5%
Total number of payments = 19 x 12 = 228
Using the same formula as above: 
Monthly payment = 135800 * 0.005 * (1 + 0.005)^228 / [(1 + 0.005)^228 - 1] = $1,582.04
Total of monthly payments = 1,582.04 x 228 = $360,019.12 (rounded to the nearest cent)

Therefore, the best choice is E, with the 15-year mortgage costing more than the 19-year mortgage in total monthly payments.

One Lender Offers Two Mortgages, a 15-Year Mortgage at 16 $341,058.75,19\$ 341,058.75,19$341,058.75,19

One Lender Offers Two Mortgages, a 15-Year Mortgage at 16 $\$ 341,058.75,19$