Chapter 5.7, Problem 54AYU

Analyzing Interest Rates on a Mortgage Colleen and Bill have just purchased a house for $\$650,000$, with the seller holding a second mortgage of $\$100,000$. They promise to pay the seller $\$100,000$ plus all accrued interest 5 years from now. The seller offers them three interest options on the second mortgage:

(a) Simple interest at $6\%$ per annum

(b) $5.5\%$ interest compounded monthly

(c) $5.25\%$ interest compounded continuously Which option is best? That is, which results in paying the least interest on the loan?

To determine

To find: Analyzing Interest Rates on a Mortgage Colleen and Bill have just purchased a house for $\$650,000$, with the seller holding a second mortgage of $\$100,000$. They promise to pay the seller $\$100,000$ plus all accrued interest 5 years from now. The seller offers them three interest options on the second mortgage:

a. Simple interest at $6\%$ per annum.

b. $5.5\%$ interest compounded monthly.

c. $5.25\%$ interest compounded continuously.

Which option is best? That is, which results in paying the least interest on the loan?

Answer to Problem 54AYU

Solution:

Simple interest with $6\%$ per annum is best.

Explanation of Solution

Given:

$P=\$1,00,000, t=5$

Calculation:

a. Simple interest at $6\%$ per annum

$I=prt$

$=100000\times 0.06\times 5$

$=30000$

Total amount after 5 years $=1,30,000$

b. $5.5\%$ interest compounded monthly

$A=P{\left(1+\frac{r}{n}\right)}^{nt}$

$A=100000{\left(1+\frac{0.055}{12}\right)}^{5\left(12\right)}$

$=1,31,570.38$

Total amount after 5 years $=1,31,570$

c. $5.25\%$ interest compounded continuously

$A=P{e}^{rt}$

$A=100000e^{0.0525\left(5\right)}$

$=1,30,017.65$

Total amount after 5 years $=1,30,018$