Answer:
a. $ 4,276.86
b. $ 680.19
c. $ 6,000
d. $ 4,704.55
e. $ 714.20
f. $ 6,000
Step-by-step explanation:
The following formula applies to the first two items:
[tex]FV=P[\frac{(1+r)^{n}-1 }{r} ][/tex]
Where:
P = Periodic payment.
r = rate per period.
n = number of periods.
a. $ 200 per year for 12 years at 10%.
In this case: P = $200, r = 10% or 0.1, and n = 12
We replace in the FV formula:
[tex]FV = 200[\frac{(1+0.1)^{12}-1 }{0.1} ][/tex]
[tex]FV=200[ \frac{1.1^{12} -1}{0.1} ][/tex]
[tex]FV=200[\frac{2.138428}{0.1} ][/tex]
[tex]FV=200*21.384284[/tex]
[tex]=4,276.86[/tex]
b. $100 per year for 6 years at 5%.
In this case: P = $100, r = 5% or 0.05, and n = 6.
We replace in the FV formula:
[tex]FV = 100[\frac{(1+0.05)^{6}-1 }{0.05} ][/tex]
[tex]FV=100[ \frac{1.05^{6} -1}{0.05} ][/tex]
[tex]FV=100[\frac{0.3400956406}{0.05} ][/tex]
[tex]FV=100*6.8019128[/tex]
[tex]=680.19[/tex]
c. $600 per year for 10 years at 0%.
If the interest rate is 0%, simply multiply the amount of money by the number of years during which it will be received.
In this case: P = $600, and n = 10
[tex]FV=600*10[/tex]
[tex]FV=6000[/tex]
For the items d. and e., the Future Value of Annuity Due must be applied.
[tex]FVAD=(1+r)*P[\frac{(1+r)^{n}-1 }{r} ][/tex]
It is the same as saying:
[tex]FVAD=(1+r)*FV[/tex]
d. $200 per year for 12 years at 10%.
In this case: P = $200, r = 10% or 0.1, n = 12, and FV = 4,276.86 (We obtained this in a. ).
We replace in the FVAD formula:
[tex]FVAD=(1+0.1)*(4,276.86)[/tex]
[tex]FVAD=(1.1)*(4,276.86)[/tex]
[tex]FVAD=4,704.546[/tex]
FVAD = 4,704.546 or (rounded) 4,704.55
e. $100 per year for 6 years at 5%.
In this case: P = $100, r = 5% or 0.05, n = 6, and FV = 680.2 (We obtained this in b. ).
We replace in the FVAD formula:
[tex]FVAD=(1+0.05)*(680.19)[/tex]
[tex]FVAD=(1.05)*(680.19)[/tex]
[tex]FVAD=714.1995[/tex]
FVAD = 714.1995 or (rounded) 714.20.
f. $600 per year for 10 years at 0%
Because the interest rate is 0, the ordinary annuity is exactly the same as the due one, that is, $ 6,000.
