Question

A loan of ​$5103 borrowed today is to be repaid in three equal installments due in one year​, four ​years, and five-and-a-half​years, respectively. What is the size of the equal installments if money is worth 4.8% compounded quarterly?

Answer 1

To calculate the size of the equal installments, we can use the present value of an annuity formula. The present value is $5103, the interest rate is 4.8% compounded quarterly, and the total number of years is 10.5.

Step-by-step explanation:

To calculate the equal installments, we can use the formula for the present value of an annuity:

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

Where:

• PV is the present value or loan amount - $5103
• PMT is the size of the equal installments
• r is the interest rate per period - 4.8% compounded quarterly, so r = 4.8% / 4 = 1.2%
• n is the number of compounding periods per year - 4
• t is the total number of years - 1 + 4 + 5.5 = 10.5

Now we can simply plug in the values and solve for PMT:

PV = PMT * [(1 - (1 + 0.012 / 4)^(-4 * 10.5)) / (0.012 / 4)]

Solving this equation will give us the size of the equal installments.