Question

(1 point) Recall that the formula for a simple interest amortized loan, with initial loan value Vo, monthly payments of size m, with interest compounded n times per year for t years at annual interest rate r is rtn.t rt Ben buys his $230,000 home and, after the $40,000 down payment, finances the remainder with a simple interest amortized loan. Ben can pay at most $1,200 per month for the loan, on which the lender has set an annual rate of 5%, which is compounded monthly Ben will have his home loan paid off in about years and months (rounding up).

Answer 1

price of house is 230000

down payment is 40000

loan amount is 230000-40000=190000

V₀=190000

m=1200

r = 5% = 0.05

n=12 for monthly compound

t= years?

put all value in given equation

0.05 12t 0.05 12-t 190000 | 1 + = 1200 | 1.05 12

(1+0.004167)12t- 1 +0.004167)12 -1 190000 (1+0.004167)12 1200 1 0.004167

(1.004167) 12t-1 190000 (1.004167)12t-1200 0.004167

1200 190000 (1.004167)12 0.004167 (1.004167)122-1

12t 288000 [(1.004167)2t- 1 190000 (1.004167)12

190000 238000 1.004[(1.004167)12

0.6597 (1.004 16712tー(1.004167)12t -1

0.6597 (1.004167)はー(1.004167)は一一1

0.34027 (1.004167)12--1

0.34027 (1.004 16712t-1

1.00416712 0.34027

$\left(1.004167\right)^{12t}=2.93877$

712t In (1.004167 (2.93877)

$12t\ln \left(1.004167\right)=\ln \left(2.93877\right)$

$t=\frac{\ln \left(2.93877\right)}{12\ln \left(1.004167\right)}$

$t=\frac{1.077993}{0.0499}$

${\color{Red} t=21.6029}$ years

that is around 21 years and 7 months