Question

Monty borrowed $10,500 and promises to make three equal payments, one in 6 months, one in 12 months, and one in 18 months. If money is worth 10% compounded quarterly, what is the size of the equal payments? Use 18 months as the focal date.

Answer 1

The money will be paid in three equal shares of $4056.48.

Explanation:

This is a compound interest problem

Compound interest formula:

The compound interest formula is given by:

`A = P(1 + (r)/(n))^(nt)`

A: Amount of money(Balance)

P: Principal(Initial deposit)

r: interest rate(as a decimal value)

n: number of times that interest is compounded per unit t

t: time the money is invested or borrowed for

In our problem, we have

A: The amount of money that will have to be paid

P = $10,500(The initial money)

r = 0.1

n = 3(the money is compounded each 4 months, and there 12 months a year, so the money is compounded 3 times a year).

t = 1.5(18 months is a year and half)a year.

So:

`A = 10,500(1 + (0.1)/(3))^(3*1.5)`

`A = $12,169.46`

$12,169.46 is the amount of money that Monty will have to pay. It will be paid in 3 equal shares of 12,169.46/3 = $4056.48.