- 20 Marks
Question
a) A petty trader has expressed interest in the purchase of a flat screen TV set from Mr. Obudan, a vendor who operates a hire purchase business. A TV set worth GHS780 may be purchased from Mr. Obudan by making GHS80 down payment and the balance in monthly installments for 2 years.
(i) Explain (in your own words) the term “charges 15% (per annum) compounded monthly” to the petty trader. [5 Marks]
(ii) Calculate the monthly installment of Mr. Obudan charges 15% compounded monthly, and the first installment is due in one month. [7 Marks]
(b) The petty trader has made semiannual deposits of GHS500 for 5 years into a savings fund paying interest. at 6.25% (per annum) compounded semiannually.
(i) Explain (in your own words) the term “charges 6.25% (per annum) compounded seminally” to the petty trader. [5 Marks]
(ii) Calculate the amount to be deposited semiannually for 2 years to bring the fund up to GHS 10,000,00. [8 Marks]
Answer
(a) (i) “Charges 15% per annum compounded monthly” means the vendor adds 15% interest yearly on the unpaid balance, but calculates and adds it monthly (1.25% per month), so interest earns interest each month, increasing the total cost faster than simple interest. For the trader, this makes repayments higher, like in Ghanaian microfinance loans under BoG regulations.
(ii) Balance=700. Monthly r=0.15/12=0.0125, n=24. Installment PMT=700 * [r(1+r)^n / ((1+r)^n -1)] ≈ GHS33.94. To arrive: Annuity formula for loan payment; compute (1+0.0125)^24≈1.348, then PMT=700*(0.0125*1.348)/(1.348-1)≈33.94.
(b) (i) “Charges 6.25% per annum compounded semi-annually” means the fund adds 6.25% interest yearly, but splits into two periods (3.125% every 6 months), with interest on interest twice a year, growing savings faster. For the trader, this boosts returns, similar to savings accounts in Ghanaian banks post-DDEP recovery.
(ii) Semi r=0.03125, past FV=500*((1.03125)^10 -1)/0.03125≈5765.05. After 4 more periods: 5765.05*(1.03125)^4≈5765.05*1.131≈6519. Future annuity factor=((1.03125)^4 -1)/0.03125≈4.26. X=(10000-6519)/4.26≈830.22. To arrive: FV past via annuity FV formula; grow it; solve for X in annuity FV= target – grown past.
- Tags: Annuity, Compound Interest, Hire Purchase, installment calculation, savings fund
- Level: Level 2
- Uploader: Samuel Duah