Question

Use Excel to answer this question

3 Part 1 (8 marks) 4 Suppose you receive $100 at the end of each year for the next three years. 5 6 a. (2 marks) 7 If the interest rate is 8% per annum (interest paid annually), what is the present value of these cash flows? 8 9 b. (2 marks) 10 What is the future value in three years of the present value you computed in part (a)? 11 12 c. (2 marks) 13 Assume that no withdrawals are made from the savings account until the end of the third year. What is the interest component? 14 15 d. (2 marks) 16 Compute the effective 3 years rate (total interest over 3 years). Hint: EFFECT function is not appropriate for this part as it is often used to compute an effective annual interest rate from a nominal interest rate.

Answer 1

Part A:

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$         100.00
Int Rate	8.000%
Periods	3

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 100 * [ 1 - [(1+0.08)^-3]] /0.08
= $ 100 * [ 1 - [(1.08)^-3]] /0.08
= $ 100 * [ 1 - [0.7938]] /0.08
= $ 100 * [0.2062]] /0.08
$257.71

Part B:

Future Value:
FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Present Value	$         257.71
Int Rate	8.0000%
Periods	3

Future Value = Present Value * ( 1 + r )^n
= $ 257.71 ( 1 + 0.08) ^ 3
= $ 257.71 ( 1.08 ^ 3)
= $ 257.71 * 1.2597
= $ 324.64

Part C:

Int = FV - Amounts deposited

= $ 324.64 - $ 300

= $ 24.64

Part D:

Effective Rate:

Effective Int Rate = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.08 ) ^ 3 ] - 1
= [ ( 1.08 ) ^ 3 ] - 1
= [ 1.2597 ] - 1
= 0.2597
I.e Effective Int Rate is 25.97 %