Question

You want to buy a $183,000 home. You plan to pay 15% as a down payment, and take out a 30 year loan for the rest. a) How much is the loan amount going to be? b) What will your monthly payments be if the interest rate is 6%? c) What will your monthly payments be if the interest rate is 7%?

Answer 1

First, let's find 15% of 183,000.

$0.15\cdot183,000=27,450$

The down payment is $27,450.

(a) To find the amount of the loan, we just have to subtract.

$183,000-27,450=155,550$

Hence, the loan amount is $155,550.

(b) The monthly payment formula is

$M=\frac{i\times P\times(1+i)^n}{(1+i)^n-1}$

Where P = 155,550. i = 0.06/12. n = 360 (number of payments). Let's replace these values.

$\begin{gathered} M=\frac{0.005\times155,550\times(1+0.005)^{360}}{(1+0.005)^{360}-1} \\ M=\frac{777.75(6.02)}{6.02-1}=\frac{4,682.06}{5.02}=932.68 \end{gathered}$

Hence, the monthly payment is $932.68.

(c) We repeat the process but instead of using 6% interest, we are going to use 7% interest.

P = 155,550.

i = 0.07/12.

n = 360.

Then, we replace the values in the formula.

$\begin{gathered} M=\frac{0.0058\times155,550\times(1+0.0058)^{360}}{(1+0.0058)^{360}-1} \\ M=\frac{902.19(8.02)}{8.02-1}=\frac{7,235.56}{7.02}=1,030.71 \end{gathered}$

Hence, the monthly payment is $1,030.71 with 7% interest.