Question

Business Mathematics answers the questions show the steps based on a formula.

4. Use formulas to find the present value for each of the following:

	Future Value	Rate	Number of Years	Compounded	Present Value
1	$1	10%	5	Annually	?
2	$1	12%	8	Semi-annually	?
3	$1	6%	10	Quarterly	?
4	$1	12%	2	Monthly	?

5. Ahmed borrowed AED30,000 for office furniture. The loan was for six months at an annual interest rate of 8%. What are Ahmed’s interest and maturity value?

6. On March 4, Saleh borrowed AED50,000 at 5% interest. Interest and principal are due on July 6. What is the interest cost and the maturity value?

Answer 1

Part 1)

Future value (FV) = $1; rate (r) = 10% per annum; Period (n) = 5years;

Present value (PV) = FV/[(1+r)^n] = 1/[(1+0.1)^5] = 1/(1.1^5) = 1/1.61051 = $0.6209

Part 2)

Future value (FV) = $1; rate (r) = 12% per annum = 12%/2 = 6% per half year; Period (n) = 8years = 8*2 = 16 semi annual period;

Present value (PV) = FV/[(1+r)^n] = 1/[(1+0.06)^16] = 1/(1.06^16) = 1/2.540351685 = $0.3936

Part 3)

Future value (FV) = $1; rate (r) = 6% per annum = 6%/4 = 1.5% per quarter; Period (n) = 10years = 10*4 = 40 quarters;

Present value (PV) = FV/[(1+r)^n] = 1/[(1+0.015)^40] = 1/(1.015^40) = 1/1.814018409 = $0.5513

Part 4)

Future value (FV) = $1; rate (r) = 12% per annum = 12%/12 = 1% per month; Period (n) = 2years = 2*12 = 24month;

Present value (PV) = FV/[(1+r)^n] = 1/[(1+0.01)^24] = 1/(1.01^24) = 1/1.269734649 = $0.7876

Part 5)

Ahamed borrowing (PV) = AED 30,000; Assumed compounded semi-annually; Interest rate (r) = 8% = 8%/2 = 4% per half year; Period (n) = 1 half year

Maturity value = PV*[(1+r)^n] = 30000*[(1+0.04)^1] = 30000*1.04 = AED 31,200

Ahamed interest = Maturity value - Borrowing = AED 31,200 - AED 30,000 = AED 1,200

Part 6)

Assumed loan is based on simple interest method.

Saleh borrowings (PV) = AED 50,000; rate (r) = 5% per annum; Days (n) = 4th march to July 6 = 125days

Interest = PV * r * n/365 = 50000*(5/100)*125/365 = 2500*125/365 = AED 856.16

Maturity value = PV+interest = AED 50,000 + AED 856.16 = AED 50,856.16