Question

Q1: For each of the following:

Compute the Future value (FV)

Present Value	Years	Interest rate	Future Value
$ 3,159 84,53 89,305	T 16 19 26	13% Y 9 5
Compute Present Value	15 8 13 25	7% 11 10 13	$ 17,328 41,517 7903,82 647,816
Compute the interest rate
Present Value	Years	Interest rate	Future Value
$ 715 905 15,000 70,300	11 8 23 16		$ 1,381 1,718 141,832 312,815

Q2: Compute the Future value of $ 1,000 continuously c compounded 12 percent for:

5 years at a stated annual interest rate of

12 percent;

3 years at a stated annual interest rate of 10 percent.

10 years at a stated annual interest rate of 5 percent;

and

8 years at stated annual interest rate of 7 percent

Q3: Consider a firm with a contract to sell an asset for $ 115,000 three years from now, the asset costs $ 72,000 to produce today. Given a relevant discount rate on this asset is 13 percent per year. Will firm make a profit on this asset? At what interest rate does the firm just break even?

Answer 1

Formula to be used in all the questions is,

Future Value = Present Value * ( 1+ Interest Rate )^ (no of years)

Answer 1.1)

Future Value = Present Value * ( 1+ Interest Rate )^ (no of years)

Present Value	Years	Interest	Future Value	Future Value
3159	16	13%	= (3159)*(1+13%)^16	22325.68
8453	19	9%	= (8453)*(1+9%)^19	43462.46
89305	26	5%	= (89305)*(1+5%)^26	317539.35

Answer 1.2)

Present Value = Future Value / ( 1+ Interest Rate )^ (no of years)

Present Value = (17328)/(1+7%)^15 = 6280.46

Years	Interest	Future Value	Present Value
15	7%	17328	6280.46
8	11%	41517	18015.33
13	10%	790382	228945.51
25	13%	647816	30513.40

Answer 1.3)

PV	Years	FV
715	11	1381
905	8	1718
15000	23	141832
70300	16	312815

Lets take the first case,

FV = PV * ( 1+i)^n

1381 = 715 * ((1+i) ^ 11

divide above equation by 715

1381/715 = (1+i)^11

1.93 = (1+i)^11

lets multuply by power of 1/11 with both sides,

1.93^1/11 = 1+i

1.0616 = 1+i

i = 1 - 1.0616 = 6.16%

In similar way remaining values have been calculated,

PV	Years	FV	FV/PV	(FV/PV)^(1/n)	i
715	11	1381	1.931468531	1.061670586	6.17%
905	8	1718	1.898342541	1.083419935	8.34%
15000	23	141832	9.455466667	1.102607643	10.26%
70300	16	312815	4.449715505	1.097793779	9.78%

Asnwer 2)

Future Value = Present Value * (1+i)^n

PV	i	n	FV
1000	12%	5	1762.34
1000	10%	3	1331.00
1000	5%	10	1628.89
1000	7%	8	1718.19

Answer 3)

Future Value = 115000

Asset costs today = 72000

Interest = 13%

No of years = 3 years

let us calculate the present value

PV = FV / (1+i)^n

= 115000 / (1+13%)^3

PV = 79700.76

We can conclude than present value of asset is higher than cost today hence firm will not make a profit of given scenario.

With trial amd error method, 16.89% should be the interest rate for breakeven the cost with 3 year period.