Consider a series of end-of-period CFs spanning 2042-2051, which decrease at a 0.6% rate each period....

Consider a series of end-of-period CFs spanning 2042-2051, which decrease at a 0.6% rate each period. The amount of the first CF in the series is $140. The interest rate is 2.1%. What is the equivalent value of this series at the end of 2051?

Solutions

Expert Solution

The amount of the First CF in the series is $140 and the interest rate initially is 2.1% which is getting decreased by 0.6% with each period passes.

Assuming the given data is for the starting period so calculating the equivalent value for the period ending with 2042

Step 1: 2.1- (0.6/100)= 2.094%; [ as 0.6% is getting deducted in each period]

Step 2: 140*(2.094/100)= 2.9316

Equivalent value ending first period will be: 140+2.9316= $142.93

Calculating Equivalent value for the period ending 2043: Step No. 1 will be same because 0.6% is getting decreased with the end of each period.

Step 2: 142.93*(2.094/100)= 2.99; Equivalent Value for the period ending 2043 will be 142.93+2.99= 145.92

Calculating Equivalent value for the period ending 2044: Step No. 1 will be same because 0.6% is getting decreased with the end of each period.

Step 2: 145.92*(2.094/100)= 3.05; Equivalent Value for the period ending 2044 will be 145.92+3.05= 148.97

Calculating Equivalent value for the period ending 2045: Step No. 1 will be same because 0.6% is getting decreased with the end of each period.

Step 2: 148.97*(2.094/100)= 3.11; Equivalent Value for the period ending 2045 will be 148.97+3.11= 152.08

Calculating Equivalent value for the period ending 2046: Step No. 1 will be same because 0.6% is getting decreased with the end of each period.

Step 2: 152.08*(2.094/100)= 3.18; Equivalent Value for the period ending 2046 will be 152.08+3.18= 155.26

Calculating Equivalent value for the period ending 2047: Step No. 1 will be same because 0.6% is getting decreased with the end of each period.

Step 2: 155.26*(2.094/100)=3.25 ; Equivalent Value for the period ending 2047 will be 155.26+3.25= 158.51

Calculating Equivalent value for the period ending 2048: Step No. 1 will be same because 0.6% is getting decreased with the end of each period.

Step 2: 158.51*(2.094/100)= 3.31; Equivalent Value for the period ending 2048 will be 158.51+3.31= 161.82

Calculating Equivalent value for the period ending 2049: Step No. 1 will be same because 0.6% is getting decreased with the end of each period.

Step 2: 161.82*(2.094/100)= 3.38; Equivalent Value for the period ending 2049 will be 161.82+3.38= 165.20

Calculating Equivalent value for the period ending 2050: Step No. 1 will be same because 0.6% is getting decreased with the end of each period.

Step 2: 165.20*(2.094/100)= 3.45; Equivalent Value for the period ending 2050 will be 165.20+3.45= 168.65

Calculating Equivalent value for the period ending 2051: Step No. 1 will be same because 0.6% is getting decreased with the end of each period.

Step 2: 168.65*(2.094/100)= 3.53; Equivalent Value for the period ending 2051 will be 168.65+3.53= 172.18

jeff jeffy answered 8 months ago

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