Answer to Question #218553 in Financial Math for Thabang Lebeko

Question

Mike wants to buy a scooter that costs R10 000,00, but he cannot afford to buy it cash. He opts for the hire purchase agreement, which requires a 13% deposit and 24 equal monthly instalments at an interest rate of 15% per annum, compounded monthly. Answer the following questions: a) How much will his deposit be? b) Calculate the total amount that he still must pay after the deposit. c) Calculate the monthly instalments.

Answer 1

Mike's deposit is 13% on total price,

So,

Deposit = 0.13 ×10,000 = 1,300

Mike's deposit for the scooter is 1,300.

If mike pays the deposit, his remaining amount will be,

10,000 $-$ 1,300 = 8,700

Thus,

Total amount that mike still has to pay after deposit is 8,700.

However, mike will end up paying higher than this as he is paying 15% interest per annum on this for 2 years.

To find the monthly installment amount, we will use the following formula

$P = \frac {PV _{annuity}} {[\frac { (1- (1+r)^{-n} )} {R} ]}$

Where:

P = periodic payment

PV annuity = present value of annuity (Loan amount)

r = interest rate

n = number of periods.

As we want to find the monthly installment, we will divide the interest rate by 12, and take 24 as number of periods.

r = 15%/12 = 1.25%

Now let's plug in the number in the formula:

$P =\frac {8700} {[ \frac {(1- (1+0.0125)^{-24} )} {0.0125}] }$

$=\frac {8700} {[\frac {(1- 0.742197069 )} {0.0125}]}$

$=\frac {8700} {\frac {(0.257802931}{0.0125)}}$

= $\frac {8700} {20.62423451}$

= 421.83

Thus,

Mike's monthly installment will be 421.83.

To find the how much total amount mike will end up paying more,

Extra amount paid = total amount $-$ loan amount

Total amount = 421.83 × 24 = 10,124.01

Extra amount paid = 10,124.01 $-$ 8,700=1,424.01

Thus, mike will end paying 1,424.01 more.