1 answer

(1 point) Recall that the formula for a simple interest amortized loan, with initial loan value Vo, monthly payments of

Question:

(1 point) Recall that the formula for a simple interest amortized loan, with initial loan value Vo, monthly payments of size

(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).

Answers

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

.

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