Question

Find the present value of $600 due in the future under each of these conditions: 6% nominal rate, semiannual compounding, discounted back 9 years. Round your answer to the nearest cent. $ 6% nominal rate, quarterly compounding, discounted back 9 years. Round your answer to the nearest cent. $ 6% nominal rate, monthly compounding, discounted back 1 year. Round your answer to the nearest cent. $ Why do the differences in the PVs occur

Answer 1

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