Question

1) What is the present value of $9,065,725, discounted at 12.74% for 5 years, compounded annually?

2) You are offered an investment that will pay you a total of $8,816,338 in 11 years. You can otherwise invest your money in similar investments that earn 2.68%, compounded annually. What's the most you'd be willing to pay for this investment?

3)How much simple interest is earned on $92,089 at 9.24% over 14 years?

4) You invested $84,279 in a savings account earning 0.19% in simple interest. How much interest will you earn over 8 years if she does not reinvest the interest?

5) What is the future value in year 19 of $697,536,062 in year 1, invested at 0.87%?

6) You have been promised a retirement bonus of $36,962 in 10 years. You expect to be able to invest that money at 7.67% for the next 8 years. How much money will you have after 8 years?

Answer 1

Present Value:

Present value is current value of Future cash flows discounted at specified discount Rate.

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

Part 1:

Particulars	Amount
Future Value	$      9,065,725.00
Int Rate	12.7400%
Periods	5

Present Value = Future Value / ( 1 + r )^n
= $ 9065725 / ( 1 + 0.1274 ) ^ 5
= $ 9065725 / ( 1.1274 ) ^ 5
= $ 9065725 / 1.8213
= $ 4977512.84

Part 2:

Max amount that can be paid is PV of CFs.

Particulars	Amount
Future Value	$      8,816,338.00
Int Rate	2.6800%
Periods	11

Present Value = Future Value / ( 1 + r )^n
= $ 8816338 / ( 1 + 0.0268 ) ^ 11
= $ 8816338 / ( 1.0268 ) ^ 11
= $ 8816338 / 1.3377
= $ 6590885.57

Part 3:

Int = PTR
P = Principal
T = Time
R = Rate of int

Particulars	Amount
Principal	$ 92,089.00
Time Period ( In Years)	14
Rate of Int	9.24%

Int = PTR
= $ 92089 * 14 * 9.24 %
= $ 119126.33

Int for 14 Years is $ 119126.33

Part 4:

Int = PTR
P = Principal
T = Time
R = Rate of int

Particulars	Amount
Principal	$ 84,279.00
Time Period ( In Years)	8
Rate of Int	0.19%

Int = PTR
= $ 84279 * 8 * 0.19 %
= $ 1281.04

Int for 8 Years is $ 1281.04

Part 5:

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

Particulars	Amount
Present Value	$ 697,536,062.00
Int Rate	0.8700%
Periods	18

Time period = 19 years - 1 Years

= 18 Years

Future Value = Present Value * ( 1 + r )^n
= $ 697536062 ( 1 + 0.0087) ^ 18
= $ 697536062 ( 1.0087 ^ 18)
= $ 697536062 * 1.1687
= $ 815,235,419.3

Part 6:

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

Particulars	Amount
Present Value	$           36,962.00
Int Rate	7.6700%
Periods	8

Future Value = Present Value * ( 1 + r )^n
= $ 36962 ( 1 + 0.0767) ^ 8
= $ 36962 ( 1.0767 ^ 8)
= $ 36962 * 1.8062
= $ 66,759.51