What is the future value of an ordinary annuity with equal payments of $450 bein

ID: 2758063 • Letter: W

Question

What is the future value of an ordinary annuity with equal payments of $450 being deposited into a money market account at the end of every year for three years if the interest rate is 7% and compounds once per year?

What is the present value of a 4-year uneven cash flow stream with $6500, $8200, $8400 and $32800 to be received the first, second, third and fourth years if the interest rate is 9% and compounds once per year?

If you take out a bank loan with a 17% quoted nominal interest rate that is compounded semiannually what is the effective annual rate (EAR)? What is the EAR if the loan compounds continuously?

Explanation / Answer

Answer 1

Because Interest is compounded once in a year, period (n) shall be 3 years and annual Interest rate (i) will be 7%

Future Value= Present Value*[Future Value factor for n=3, i=7%]

Future Value= 450*[1.2250]

Future Value= 551.25

Answer 2

Years

Future Value (FV)

Present value (PV)

Future value factor

6500

6500/[FV for n=1, i=9%]

1.09

5963.303

8200

8200/[FV for n=2, i=9%]

1.1881

6901.776

8400

8400/[FV for n=3, i=9%]

1.295

6486.486

32800

32800/[FV for n=4, i=9%]

1.5388

21315.31

Total

40666.88

Answer 3

effective annual rate=(1+i/n)-1

Where

i= annual interest rate &

n= no. of compounding periods

Since Loan compounds semiannually, period (n) shall be 2 and rate (i) shall be 17/2 i.e 8.5% semiannually

effective annual rate=(1+.17/2)2-1

effective annual rate=17.72%

Effective annual rate when interest componded continously=er-1

Effective annual rate when interest componded continously=18.53%