Question

​(Compound interest with​ non-annual periods​) You just received a bonus of ​$5 comma 000. a.  Calculate the future value of ​$5 comma 000​, given that it will be held in the bank for 5 years and earn an annual interest rate of 6 percent. b.  Recalculate part ​(a​) using a compounding period that is​ (1) semiannual and​ (2) bimonthly. c.  Recalculate parts ​(a​) and ​(b​) using an annual interest rate of 12 percent. d.  Recalculate part ​(a​) using a time horizon of 12 years at an annual interest rate of 6 percent. e.  What conclusions can you draw when you compare the answers in parts ​(c​) and ​(d​) with the answers in parts ​(a​) and ​(b​)? a.  What is the future value of ​$5 comma 000 in a bank account for 5 years at an annual interest rate of 6 ​percent? ​$ 32768.5  ​(Round to the nearest​ cent.) b.  What is the future value of ​$5 comma 000 in a bank account for 5 years at 6 percent compounded​ semiannually? ​$ nothing  ​(Round to the nearest​ cent.) What is the future value of ​$5 comma 000 in a bank account for 5 years at 6 percent compounded​ bimonthly? ​$ nothing  ​(Round to the nearest​ cent.)

Answer 1

a) 6,691.13

b) semiannually: 6,719.58

bi-monthly 6,739.24

c) 5,000 at 12% annual, semiannual adn bi-monthly

8,811.71 /// 8,954.24 /// 9,056.81

d)

5,000 at 6% for 12 years

`5000 \: (1+ 0.06)^(12) = Amount`

Amount 10,060.98

e) conclusion:

the amount increases as the rate increase his compounding

the amount increase as rate increase

the amount increase as time increase.

Step-by-step explanation:

We solve using future value of a lump sum formula:

`Principal \: (1+ r)^(time) = FV`

Principal 5,000.00

time 5.00

rate 0.06000

`5000 \: (1+ 0.06)^(5) = FV`

Amount 6,691.13

b.- we adjust rate and time for the total compounding.

time 10.00 (5 years / 2 compounding)

rate 0.03000 (6% divide into 2)

`5000 \: (1+ 0.03)^(10) = Amount`

Amount 6,719.58

time 30.00

rate 0.01000

`5000 \: (1+ 0.01)^(30) = Amount`

Amount 6,739.24

for c) we recalcuate all over again but, with double rate.

for d) we calcualte 5,000 for 12 year at 6%