Question

Bongeka purchased a new refrigerator and were expected to pay R1 684,00 five months ago and another R1 323,00 in eight months’ time. She could not make the payment five months ago, but after receiving a bonus at work, she rescheduled to repay the loan in two equal payments, the first due in two months and the second due in five months’ time. The payment at month five will settle the debt, therefore, the settlement date is month five. The debts and payments are subject to the same interest rate of 11,4% per annum, compounded monthly.

Answer 1

The discount factor computed shows that the value of each payment will be $1546.

How to calculate the payment?

The following can be deduced from the information:

Payment due in 5 months = $1684

Payment due in 8 months = $1323

Annual interest  = 11.40%

Monthly interest rate = 11.40%/12 = 0.95%

Present value of payment due 5 months ago = $1684 + (1 + 0.95%)⁵ = $1765.52

Present value of payment due 8 months ago = $1226.62

Total present value = $1765.52 + $1226.62 = $2992.14

After rescheduling, the payments will be in 2 months and 5 months.

Discount factor for payment due in 2 months = 0.9813

Discount factor for payment due in 5 months = 0.9538

Combined discount factors= 0.9360

Therefore, the value of each payment will be:

= $2992.14/(1 + 0.9360)

= $1546

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