Question

You have an investment account that started with $1200 12 years ago and now has grown to $7500. What annual interest rate have you earned? Assume you made no additional contributions to the account. Assume an annually compounded interest rate. (round to two decimals)

Find the future value of an ordinary annuity that pays $600 per year for 4 years at 5%. Compounding occurs once a year.

Find the future value of an initial $2,550 compounded for 6 years at 3%. Assume annual compounding. (round to the nearest whole dollar)

What is the present value of an ordinary annuity that pays $550 per year for 11 years at 5%? Assume annual compounding

Consider a perpetuity with the first cash flow at the end of year 1. If the invested funds of the perpetuity could earn 9% per year and the perpetuity paid $384 per year, what is the present value of the perpetuity? (round to the nearest dollar)

Answer 1

a

Int rate Calculation
Particulars	Amount
Present Value	$       1,200.00
Future Value	$     26,958.00
Years	12

Future Value = Cash Flow * ( 1 + r )^n
$ 26958 = $ 1200 ( 1 + r ) ^ 12
( 1 + r ) ^ 12 = $26958 / $1200
( 1 + r ) ^ 12 = 22.465
( 1 + r ) = 22.465 ^ ( 1 / 12 )
( 1 + r ) = 1.2961
r = 1.2961 - 1
r = 0.2961 i.e 29.61 %

b

FV of Annuity
Particulars	Amount
Cash Flow	$         600.00
Int Rate	5.000%
Years	4

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 600 * [ [ ( 1 + 0.05 ) ^ 4 ] - 1 ] / 0.05
= $ 600 * [ [ ( 1.05 ) ^ 4 ] - 1 ] / 0.05
= $ 600 * [ [1.2155] - 1 ] / 0.05
= $ 600 * [0.2155] /0.05
= $ 2586.08

c

Future Value Calculation:
Particulars	Amount
Present Value	$                         2,550.00
Int Rate	3.0000%
Years	6

Future Value = Present Value * ( 1 + r )^n
= $ 2550 ( 1 + 0.03) ^ 6
= $ 2550 ( 1.03 ^ 6)
= $ 2550 * 1.1941
= $ 3044.83 i.e., $ 3045

d

PV of Annuity
Particulars	Amount
Cash Flow	$         550.00
Int Rate	5.000%
Years	11

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 550 * [ 1 - [(1+0.05)^-11]] /0.05
= $ 550 * [ 1 - [(1.05)^-11]] /0.05
= $ 550 * [ 1 - [0.5847]] /0.05
= $ 550 * [0.4153]] /0.05
$                  4,568.53

e

Present value of perpetuity = Cash Flow / Interest rate

= $ 384 / 9%

$ 4266.67 i.e, $ 4267

Note :

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

FV of Annuity :
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.
FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per Year
n - No. of Years

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 Year

n - No. of Years