Question

The total amount paid on a 35 year loan was $98,000. If the interest rate was 4.1% and compounded monthly, what was the principal

Answer 1

Principal = $23,392.45

Step-by-step explanation:

To solve this, we are required to find a certain amount invested for 35 years at an interest rate of 4.1% compounded annually, yielding $98,000.

The formula for compounded interest is used, and this is done as follows:

`FV=PV(1+(r)/(n) )^(nt)\\Where:\\FV=Future\ value\ =\ \$98,000\\PV= Present\ value\ =\ ???\\r= interest\ rate\ = 4.1\%=0.041\\n = number\ of\ compounding\ periods\ per\ year\ = monthly\ = \ 12\\ t= time\ =\ 35\ years`

`98000=PV(1+(0.041)/(12) )^((12*35))\\98000=PV(1+0.003417)^(420)\\98000=PV(1.003416667)^((420))\\98000=PV(4.189386)\\PV= (98000)/(4.189386) \\\\=PV= \$23,392.45`

Therefore, the principal is approximately $23,392