Question

Corporate Financial Management:The Time Value of Money

8. First City Bank pays 8 per cent simple interest on its savings account balances, whereas Second City Bank pays 8 per cent interest compounded annually. If you made a £10,000 deposit in each bank, how much more money would you earn from your Second City Bank?

2. Solve for the unknown interest rate in each of the following:

Present value (£)	Years	Interest rate (%)	Future value (£)
240	3	297
360	11	1,080

                                                                                                           

Answer 1

(8) (a) Initial Deposit = £10,000, Second City Bank Interest Rate = 8 % compounded annually, First City Bank Interest Rate = 8 % simple interest.The question does not mention the tenure of the deposit. Hence, for demonstrative purposes, it is assumed that the deposit tenure is 1 year

Therefore, First City Bank Interest = 10000 x 0.08 = £800 and Second City Bank Interest = 10000 x (1.08) - 10000 = £ 800

NOTE: This makes sense as simple and compound interest are equal for the first year of deposit.

If the deposit is extended by another year, then:

First City Bank Interest = £ 800 and Second City Bank Interest = 10800 x (1.08) - 10800 = £ 864

Extra Earnings through Second City Bank = 864 - 800 = £ 64 (which is actually an interest of 8 % earned on the previous year's interest of £800)

(b) Present Value = PV = £240, Future Value (FV) = £ 297 and Tenure = 3 years

Let the required interest rate be R%

Therefore, 240 x (1+R)^(3) = 297

R = [(297/240)^(1/3)] - 1 = 0.073615 or 7.3615% ~ 7.36 %

PV = £ 360, FV = £ 1080 and Tenure = 11 years

Let the required interest rate be Y %

Therefore, 360 x (1+Y)^(11) = 1080

Y = [(1080/360)^(1/11)] - 1 = 0.105032 or 10.5032 % ~ 10.5 %