Question

a) 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.  

I figured out the answer for part A. being 3676.389 I am unable to figure out question b.

b) If Monty misses the first payment, what will be the amount of the revised equal payments at 12 months and 18 months to pay off the debt if a renegotiated rate of 15% compounded monthly is used? Use 6 months as the focal date

Answer 1

Ans.(a)

The money will be paid in three equal shares of $4058.93.

Step-by-step explanation:

This is a compound interest problem

Compound interest formula:

The compound interest formula is given by:

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

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

So:

A = 10,500(1+0.1/4)^4*1.5

=10500(1.025)^6

=12176.78

$12,176.78 is the amount of money that Monty will have to pay.

It will be paid in 3 equal shares of 12,176.78/3 = $4,058.93.

Ans.(b)

P = $10,500

r = 0.15

n = 12

t = 6/12 =0.5 year

A = 10500(1+0.15/12)^12*0.5

=10500(1.0125)^6

=11312.52

$11,312.52 is the amount of money that Monty will have to pay.

It will be paid in 2 equal shares of 11,312.52/2 = $5,656.26.