Question

Jasmine borrowed $4758.00 compounded annually to help finance her education. She contracted to repay the loan in annual payments of $253.00 each. If the payments are due at the end of every year, and interest is 5% compounded annually, how long will Jasmine have to make annual payments? And state your answer in years and months, (from 0 to 11 months).

Answer 1

Jasmine will need to make annual payments for approximately 26 years and 7 months to pay off her loan of $4758 at a 5% annual interest rate with annual payments of $253.

Step-by-step explanation:

Jasmine borrowed $4758.00 compounded annually at an interest rate of 5%. She plans to repay this loan with annual payments of $253.00. To calculate the time it will take Jasmine to repay her loan, we can use the formula for the present value of an annuity since the loan is paid off through equal annual payments. The formula is:

PV = PMT * [(1 - (1+r)^-n) / r]

Where PV is the present value of the loan, PMT is the annual payment, r is the annual interest rate, and n is the number of payments.

Rearranging the formula to solve for n, we get:

n = -log(1 - (PV*r)/PMT) / log(1 + r)

Substituting the values into the formula:

n = -log(1 - (4758*0.05)/253) / log(1 + 0.05)

After calculating, we find the value of n to be approximately 26.61 years. Since we need the answer in years and months, the months can be determined by taking the decimal part (0.61) and multiplying it by 12, which gives approximately 7.32, or 7 months when rounded to the nearest whole month.

Therefore, Jasmine will need to make annual payments for approximately 26 years and 7 months.