Question

Calculate the future value in six years of $8,000 received today if your investments pay (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

A. 5 percent compounded annually $.
B. 7 percent compounded annually $.
C. 9 percent compounded annually $.
D. 9 percent compounded semiannually$.
E. 9 percent compounded quarterly$.

Answer 1

a) Annual effective rate = 5%

PV of payment received today = $8,000

Asked to find value in 6 years

FV of payment = PV * (1+r)^6

FV = 8000*(1.05)^6

FV = $10,720.77

b) Annual effective rate = 7%

PV of payment received today = $8,000, Asked to find value in 6 years

FV of payment = PV * (1+r)^6

FV = 8000*(1.07)^6

FV = $12,005.84

c) Annual effective rate = 9%

PV of payment received today = $8,000, Asked to find value in 6 years

FV of payment = PV * (1+r)^6

FV = 8000*(1.09)^6

FV = $13,416.80

d) 9% semi-annual compounding -> Semi-annual rate = 9%/2 = 4.5% and this needs to be compounded twice because there are 2 semi-annual periods in a year

effective rate(1+r) = (1+.045)^2

r = 9.2025%

Annual effective rate = 9.2025%

PV of payment received today = $8,000, Asked to find value in 6 years

FV of payment = PV * (1+r)^6

FV = 8000*(1.092025)^6

FV = $13,567.05

e) 9% Quarterly compounding -> Quarterly rate = 9%/4 = 2.25% and this needs to be compounded 4 times because there are 4 quarters in a year

effective rate(1+r) = (1+.0225)^4

r = 9.3083%

Annual effective rate = 9.2025%

PV of payment received today = $8,000, Asked to find value in 6 years

FV of payment = PV * (1+r)6^

FV = 8000*(1.093083)^6

FV = $13,646.13