Question

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​)?

Answer 1

Answer:

A $6,691.13

semiannual Amount $6,719.58

bimonthly Amount $6,739.24

IF bimonthly:

$Principal \: (1+ r)^{time} = Amount$

Principal 5,000.00

time 30.00

rate 0.01000

$5000 \: (1+ 0.01)^{30} = Amount$

Amount 6,739.24

IF rate is 12%

yearly Amount 8,811.71

semiaanual Amount 8,954.24

bimonthly  Amount 9,056.81

IF time is 12 years:

yearly Amount         10,060.98

semiannual Amount 10,163.97

bimonthly Amount 10,235.50

As time horizon increase

as subperiord of capitalization increases

or as rate increases

the final future value increases as well.

Explanation:

$Principal \: (1+ r)^{time} = Amount$

Principal 5,000.00

time 5.00

rate 0.06000

$5000 \: (1+ 0.06)^{5} = Amount$

Amount 6,691.13

IF semminannual:

$Principal \: (1+ r)^{time} = Amount$

Principal 5,000.00

time 10.00

rate 0.03000

$5000 \: (1+ 0.03)^{10} = Amount$

Amount 6,719.58

IF bimonthly:

$Principal \: (1+ r)^{time} = Amount$

Principal 5,000.00

time 30.00

rate 0.01000

$5000 \: (1+ 0.01)^{30} = Amount$

Amount 6,739.24

IF rate is 12%

$5000 \: (1+ 0.12)^{5} = Amount$

Amount 8,811.71

semiaanual:

$5000 \: (1+ 0.06)^{10} = Amount$

Amount 8,954.24

bimonthly:

$5000 \: (1+ 0.02)^{30} = Amount$

Amount 9,056.81

IF time is 12 years:

$5000 \: (1+ 0.06)^{12} = Amount$

Amount 10,060.98

semiannual:

$5000 \: (1+ 0.03)^{24} = Amount$

Amount 10,163.97

bimonthly:

$5000 \: (1+ 0.01)^{72} = Amount$

Amount 10,235.50