One lender offers two mortgages, a 19-year mortgage at 15%, and a 23-year mortgage at 6%.For each, find the total of the monthly payments to repay $114,200.Round to the nearest cent.
A) 19-year: $\$ 345,810.00,23$-year: $\$ 210,692.00$
B) 19-year: $\$ 345,830.88,23$-year: $\$ 210,815.29$
C) 19-year: $\$ 345,870.88,23$-year: $\$ 211,143.92$
D) 19-year: $\$ 328,539.33,23$-year: $\$ 210,815.29$
E) 19-year: $\$ 345,842.88,23$-year: $\$ 210,938.98$

Question

One lender offers two mortgages, a 19-year mortgage at 15%, and a 23-year mortgage at 6%.For each, find the total of the monthly payments to repay $114,200.Round to the nearest cent. 
A) 19-year: $\$ 345,810.00,23$-year: $\$ 210,692.00$
B) 19-year: $\$ 345,830.88,23$-year: $\$ 210,815.29$
C) 19-year: $\$ 345,870.88,23$-year: $\$ 211,143.92$
D) 19-year: $\$ 328,539.33,23$-year: $\$ 210,815.29$
E) 19-year: $\$ 345,842.88,23$-year: $\$ 210,938.98$

Quizplus · Accepted Answer

For the 19-year mortgage, the monthly payment can be calculated using the formula: 
Payment = (P * r) / (1 - (1+r)^(-n*12))
where P is the principal (amount to be borrowed), r is the monthly interest rate (15%/12), and n is the number of years (19). 
Plugging in the values, we get Payment = ($114,200 * 0.15/12) / (1 - (1+0.15/12)^(-19*12)) = $2,727.88
Multiplying this by the total number of months (19*12), we get the total amount to be repaid: $345,830.88

For the 23-year mortgage, the same formula can be used with r = 6%/12 and n = 23: 
Payment = ($114,200 * 0.06/12) / (1 - (1+0.06/12)^(-23*12)) = $1,468.76
Total to be repaid: $210,815.29

Therefore, the best choice is B.

One Lender Offers Two Mortgages, a 19-Year Mortgage at 15 $345,810.00,23\$ 345,810.00,23$345,810.00,23

One Lender Offers Two Mortgages, a 19-Year Mortgage at 15 $\$ 345,810.00,23$