Answer and Explanation:
For computing the present value we need to apply the present value formula i.e to be shown in the attachment
For the first case i.e semi annual compounding
Given that,
Future value = $600
Rate of interest = 6% ÷ 2 = 3%
NPER = 9 years × 2 = 18 years
PMT = $0
The formula is shown below:
= -PV(Rate;NPER;PMT;FV;type)
So, after applying the above formula, the present value is $352.44
For the second case i.e quarterly compounding
Given that,
Future value = $600
Rate of interest = 6% ÷ 4 = 1.5%
NPER = 9 years × 4 = 36 years
PMT = $0
The formula is shown below:
= -PV(Rate;NPER;PMT;FV;type)
So, after applying the above formula, the present value is $351.05
For the third case i.e monthly compounding
Given that,
Future value = $600
Rate of interest = 6% ÷ 12 = 0.5%
NPER = 1 years × 12 = 12 years
PMT = $0
The formula is shown below:
= -PV(Rate;NPER;PMT;FV;type)
So, after applying the above formula, the present value is $565.14
Based on the various compounding i.e semi annual, quarterly and yearly the present value would be different in each case
