Question

5. Answer the following 2 questions:   

1. How much must be invested now to provide an amount of OMR 15,000 in seven years’ time assuming interest is compounded quarterly at a nominal annual rate of 9 per cent? What is the effective annual rate?   

1. Mr. Haitham buys a vehicle on hire purchase paying 7 annual instalments of OMR1,800, the first being an immediate cash deposit. Assuming an interest rate of 9 per cent is being charged by the hire purchase company, how much is the current cash price of the vehicle?   

Answer 1

Answer to Question 5a.

Future Value = OMR 15,000

Annual Interest Rate = 9.00%
Quarterly Interest Rate = 9.00% / 4
Quarterly Interest Rate = 2.25%

Time Period = 7 years or 28 quarters

Amount Deposited = Future Value / (1 + Quarterly Interest Rate)^Time Period
Amount Deposited = OMR 15,000 / 1.0225^28
Amount Deposited = OMR 8,045

Effective Annual Rate = (1 + Quarterly Interest Rate)^4 - 1
Effective Annual Rate = (1 + 0.0225)^4 - 1
Effective Annual Rate = 1.0931 - 1
Effective Annual Rate = 0.0931 or 9.31%

Answer to Question 5b.

Annual Payments = OMR 1,800
Number of Payments = 7
Interest Rate = 9.00%

Payments are made at the beginning of each year

Cash Price = OMR 1,800 + OMR 1,800 / 1.09 + … + OMR 1,800 / 1.09^5 + OMR 1,800 / 1.09^6
Cash Price = OMR 1,800 * 1.09 * (1 - (1/1.09)^7) / 0.09
Cash Price = OMR 1,800 * 5.485919
Cash Price = OMR 9,875