Answer:
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
