Tim and Sally are taking out a personal loan to pay for their wedding expenses. The loan is for $9,000 and comes with an interest rate of 9.5% compounded monthly. The couple wants to pay the loan off as quickly as possible, keeping the monthly payments below $250. The lender offers repayment plans in 12 month increments. How long of a loan should they request?

Tim and sally should take a loan for 48 months that is for 4 years. As the number of compounding years has to be in multiples of 12, therefore n will be equal to 48 months which is 4 years.

What is the meaning of tenure in an annuity?

An amount that is required to be paid at the end of a positive duration to reach a required sum or to pay a loan is called as an annuity. Tenure of the duration wherein the amount received is paid. we have the overall components to discover any of the missing values.

To calculate the N,

[tex]\rm\,P = PMT\times [1 -\frac{\frac{1}{(1+r)^{n} } }{r}]\\[/tex]

Here, P that is principal: $9,000

PMT that is payment is equal to $250

I is interest that is 9.5%, in this case as the payment will be given monthly, therefore i = 9.5/12 = 0.7916%

n is the number of compounding years that has to be calculated in this case.

[tex]\rm\,9,000 = 250\times [1 -\frac{\frac{1}{(1+0.007917)^{n} } }{0.007917}]\\\\\\(0.992145)^n = 1- 0.285012 = 0.714988\\\\\\n = 43.4[/tex]

Thus, As the number of compounding years has to be in multiples of 12, therefore n will be equal to 48 months which is 4 years.

Learn more about annuity here:

https://brainly.com/question/5303391

#SPJ2