Question

Holly borrows $40,000 on 1/1/2022 from a bank wishes to pay it back with monthly payments of $625 at the end of each month, with the first payment made on 1/31/2022. If i⁽¹²⁾ =.072, find the number of monthly payments required to pay off the loan, and find the amount of the last payment (the last payment should be less than $625 ). Sameer wants to save enough money so that he will have $15,000 accumulated in a fund at the end of 2n years (for some unknown integer n ). Sameer deposits $204 in the fund on the last day of each of the first n years, and deposits $408 in the fund on the last day of each of the last n years. The annual effective rate of interest is i. If (1+i)ⁿ =2.0, find i.

Answer 1

To find the number of payments and the amount of the last payment for a loan, use the formula for the present value of an annuity.

Step-by-step explanation:

To find the number of monthly payments required to pay off the loan, we need to use the formula for the present value of an annuity:

PV = R(1 - (1+i)^(-n))/i

Where:

• PV is the loan amount, which is $40,000
• R is the monthly payment, which is $625
• i is the monthly interest rate, which is given by i^(12)
• n is the number of monthly payments

Substituting the given values, we have:

40,000 = 625(1 - (1+0.072)^(−n))/(0.072)

Simplifying this equation will give us the number of monthly payments, and then we can find the amount of the last payment by subtracting the sum of all previous payments from the loan amount.