Question

NO LINKS!! URGENT HELP PLEASE!!!

10. Mr. and Mrs. Rainer took out a $240,000 to purchase their home. If the interest rate on the loan is 1.2% compounded bimonthly, how much interest will they have paid after 30 years?

Answer 1

$103,875.41

Explanation:

To solve this problem, we can use the formula for compound interest:

`\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+(r)/(n)\right)^(nt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}`

Given values:

• P = $240,000
• r = 1.2% = 0.012
• n = 6 (bi-monthly)
• t = 30 years

Note: Bi-monthly means every 2 months.

Substitute the given values into the formula and solve for A:

`A=240000\left(1+(0.012)/(6)\right)^(6 \cdot 30)`

`A=240000\left(1.002\right)^(180)`

`A=343875.406934...`

`A=343875.41`

So after 30 years, Mr. and Mrs. Rainer will have paid a total of $343,875.41, which includes both the principal and the interest.

To find the amount of interest they paid, subtract the principal:

Interest paid = $343,875.41 - $240,000 = $103,875.41

Therefore, they will have paid $103,875.41 in interest over the 30-year period.