A couple borrows $A today at j₁ = 12%.The loan is to be repaid over 4-years with quarterly payments of $500,first payment due 3-months from today.If simple interest is credited for fractional interest periods,what is A?

Question

Quizplus · Accepted Answer

We can begin solving this problem by using the formula for the present value of an annuity:

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

Where PV is the present value, PMT is the periodic payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the total number of periods.

Plugging in the given values, we get:

A = 500 * [1 - (1 + 0.12/4)^(-4*4)] * (4/0.12)

Simplifying this expression, we get:

A = 500 * [1 - 0.3144] * 33.3333

A = 500 * 0.6856 * 33.3333

A = 11426.06

Therefore, the initial loan amount A is $6348.06.

A Couple Borrows $A Today at J1 = 12

A Couple Borrows $A Today at J₁ = 12