Question

Mr. Mohammed has an investment which has a nominal interest rate of 16% p.a. required:

1. Compute the effective annual interest rate if interest is received:
   1. Semi annually
   2. Quarterly
   3. After every four months
   4. Monthly
   5. Weekly
2. The amount of money invested is Sh. 100,000. It is invested for over 4 years. Compute the future value of this investment in relation to cases (i) to (v) in (a) above.

Answer 1

Part A:

Effective Annual Rate = ( 1 + r ) ^ n - 1
r = Int Rate per period
n = No.of periods per anum

1)

Particulars	Amount
Ret period	8.0000%
No. of periods	2.0000

EAR = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.08 ) ^ 2 ] - 1
= [ ( 1.08 ) ^ 2 ] - 1
= [ 1.1664 ] - 1
= 0.1664
I.e EAR is 16.64 %

2)

Particulars	Amount
Ret period	4.0000%
No. of periods	4.0000

EAR = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.04 ) ^ 4 ] - 1
= [ ( 1.04 ) ^ 4 ] - 1
= [ 1.1699 ] - 1
= 0.16986
I.e EAR is 16.986 %

3)

Particulars	Amount
Ret period	5.3333%
No. of periods	3.0000

EAR = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.053333 ) ^ 3 ] - 1
= [ ( 1.053333 ) ^ 3 ] - 1
= [ 1.1687 ] - 1
= 0.16869
I.e EAR is 16.869 %

4)

Particulars	Amount
Ret period	1.3333%
No. of periods	12.0000

EAR = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.013333 ) ^ 12 ] - 1
= [ ( 1.013333 ) ^ 12 ] - 1
= [ 1.1723 ] - 1
= 0.17227
I.e EAR is 17.227 %

5)

Particulars	Amount
Ret period	0.3077%
No. of periods	52.0000

EAR = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.003077 ) ^ 52 ] - 1
= [ ( 1.003077 ) ^ 52 ] - 1
= [ 1.1732 ] - 1
= 0.17322
I.e EAR is 17.322 %

Part B:

Future Value:

Future Value is Value of current asset at future date grown at given int rate or growth rate.

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

1)

Particulars	Amount
Present Value	$       100,000.00
Int Rate	8.0000%
Periods	8

Future Value = Present Value * ( 1 + r )^n
= $ 100000 ( 1 + 0.08) ^ 8
= $ 100000 ( 1.08 ^ 8)
= $ 100000 * 1.8509
= $ 185093.02

2)

Particulars	Amount
Present Value	$       100,000.00
Int Rate	4.0000%
Periods	16

Future Value = Present Value * ( 1 + r )^n
= $ 100000 ( 1 + 0.04) ^ 16
= $ 100000 ( 1.04 ^ 16)
= $ 100000 * 1.873
= $ 187298.12

3)

Particulars	Amount
Present Value	$       100,000.00
Int Rate	5.3333%
Periods	12

Future Value = Present Value * ( 1 + r )^n
= $ 100000 ( 1 + 0.053333) ^ 12
= $ 100000 ( 1.053333 ^ 12)
= $ 100000 * 1.8655
= $ 186547.72

4)

Particulars	Amount
Present Value	$       100,000.00
Int Rate	1.3333%
Periods	48

Future Value = Present Value * ( 1 + r )^n
= $ 100000 ( 1 + 0.013333) ^ 48
= $ 100000 ( 1.013333 ^ 48)
= $ 100000 * 1.8885
= $ 188847.74

5)

Particulars	Amount
Present Value	$       100,000.00
Int Rate	0.3077%
Periods	208

Future Value = Present Value * ( 1 + r )^n
= $ 100000 ( 1 + 0.003077) ^ 208
= $ 100000 ( 1.003077 ^ 208)
= $ 100000 * 1.8946
= $ 189461.83