Question

Find the present and future values of a constant income stream of $3000 per year over a 13 year period at 5% annual interest compounded continuously. Round your answers to the nearest cent. In particular, ROUND your answer for the Present Value to the nearest cent BEFORE using it to compute the Future Value.

a) Present Value: $

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b) Future Value: $

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Answer 1

Step 1)

we know that present value of continuous income stream that will generate I(t) dollars per year for T years at an annual interest rate of r compounded continuously is given by,

we have,

I(t) = $3000

T = 13 years

r = 5% = 0.05

Hence,

rounding to the nearest cent we can say that,

Hence we can say that present value if $28677.25

Step 2)

we know that future value of continuous income stream that will generate I(t) dollars per year for T years at an annual interest rate of r compounded continuously is given by,

we have,

I(t) = $3000

T = 13 years

r = 5% = 0.05

Hence,

rounding to the nearest cent we can say that,

Hence we can say that future value is $54932.45

Step 3)

In general we can write,

we have,

r = 0.05

T = 13

PV = $28677.25

Hence,

rounding to nearest cent we can say that,

which is same as we found in step 2)