Question

Just need to know the N, I/YR, PV, PMT, and FV values for each problem to input into financial calculator. Please specify the periods per year and if need to set in Beg or End.

-Calculate the future value of the following amounts:
a. $8,250 invested for 18 years at 5.2% per year;
b. $4,015 invested for 25 years at 14.5% per year;

-Calculate the present value:
a. $15,000 42 years from now, discounted at 8.4% per year;
b. $8,550 8 years from now, discounted at 5.2% per year;

-Calculate present value of the ordinary annuities:
a. $800 each year for 30 years, discounted 3.0% per year;
b. $5,320 each year for 26 years, discounted 8.5% per year;

-Retire in 40 years and would like to have $2,000,000 in account. (a) What amount would you have to add to your savings account at the end of each year for the next 35 years to achieve your goal if you thought that you could earn a 8% annual rate of return? (b) What amount would you have to add at the end of each year if you thought you could earn a 10% annual rate of return?

-You just got $50,000. You have decided to invest the money for the next six years. You believe that six years from now you will be able to make a purchase for $100,000. What annual rate of return will you need to achieve to make purchase?

-2 choices when you win lotto: receive $400,000 at the beginning of each year for the next 30 years, or you can receive a lump sum of $6,000,000 now. Your opportunity cost (the rate of return you can earn on any investments you make) is 6 percent per year. Ignoring any tax considerations, which option should you choose? Why?

Answer 1

1) Future Value = Present Value (1 + Interest rate)ⁿ

Where, n = Number of times compounding

a) Future Value = $8,250 (1+0.052)¹⁸

= $20,546.47

b) Future Value = $4,015 (1+0.145)²⁵

= $118,528.48

2) Present Value = Future Value / (1 + Interest rate)ⁿ

Where, n = Number of times compounding

a) Present Value = $15,000 / (1+0.084)⁴²

= $506.83

b) Present Value = $8,550 / (1+0.052)⁸

= $5,700

3) Present value of Ordinary Annuity

P = PMT [(1 - (1 / (1 + r)ⁿ)) / r]

Where:

P = The present value of the annuity stream to be paid in the future

PMT = The amount of each annuity payment

r = The interest rate

n = The number of periods over which payments are to be made

a) Present Value of ordinary annuity = $800 [(1 - (1 / (1 + 0.03)³⁰)) / 0.03]

= $15,680.35

b) Present Value of ordinary annuity = $5,320 [(1 - (1 / (1 + 0.085)²⁶)) / 0.085]

= $55,083.77

4) P = A (r / n) / [(1 + r/n)^nt - 1]

Where,

P = Savings Amount, A = Future Amount, n = No. of times compounding, t = time (years)

a) Amount that should be saved at end of each year to have $2,000,000 at end of 35 years at rate of 8%

= $10,462.56

b) Amount that should be saved at end of each year to have $2,000,000 at end of 35 years at rate of 10%

= $6,321.36

5) Future Value = $100,000 ; Present value = $50,000 ; Time (n) = 6 Years

$100,000 = $50,000 (1+r)⁶

(1+r)⁶ = 2

r = 12.25%