Question

Inflow Value QUESTION 5: The Time Value of Money alue Make use of the relevant interest and discount values provided below to determine: i) the future value (FV) of a principal of N$10 000 which you invest at 12% interest, compounded for five (5) years. ii) the present value (PV) of an amount of N$10 000, which is receivable in five (5) years from now, when the cost of capital is 12%. III) the annual deposit which is required to accumulate a future amount of N$60 000 over a period of four (4) years, when the interest rate is! 12%. iv) the annual repayments on a loan of N$100 000, repayable over five (5) years, at an interest rate of 12%. (10)

Answer 1

i)	Future Value = Present Value*((1+r)^t)
	where r is the interest rate that is 12% and t is the time period in years that is 5.
	Present value = 10000
	Future value = 10000*((1.12)^5)
	Future value = 10000*(1.762342)
	Future value = 17623.42.
	The future value is $17623.42.
ii)	Present Value = Future value/ ((1+r)^t)
	where r is the interest rate that is 12% and t is the time period in years that is 5.
	Future value = 10000
	present value = 10000/ ((1.12)^5)
	present value = 10000/(1.762342)
	present value = 5674.269
	The present value is $5674.27.
iii)	Future value of an annuity = C*[((1+r)^t-1)/r]
	where C is the annuity payment
	r is the interest rate that is 12%.
	t is the time period in years that is 4.
	Future value = 60000
	60000 = C*[((1.12)^4-1)/.12]
	60000 = C*[(1.573519-1)/.12]
	60000 = C*[(.573519)/.12]
	C*[4.779328] = 60000
	C = 12554.07
	The annual deposit is $12554.
iv)	Present value of an annuity = C*[(1-(1/(1+r)^t))/r]
	where C is the annuity payment
	r is the interest rate that is 12%.
	t is the time period in years that is 5.
	Present value = 100000
	100000 = C*[(1-(1/(1.12)^5))/.12]
	100000 = C*[(1-(1/(1.12)^5))/.12]
	100000 = C*[(1-(1/1.762342)/.12]
	100000 = C*[(1-.567427)/.12]
	100000 = C*[(.432573)/.12]
	100000 = C*[3.604776]
	C = 100000/3.604776
	C = 27740.97
	The annual repayment is $27741.