Question

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1. You plan to deposit $2,000 for the next five years with the first payment expected at...

1. You plan to deposit $2,000 for the next five years with the first payment expected at the end of the year. What is the future of the payments at the end of five years if the interest rate is expected to be 8% for the foreseeable future?

		$12,210.20
		$15,431.22
		$11,733.20
		12,568.40

1. You expect to receive the annual payments of $2,000 at the end of years 6 , 7, 8, 9 and 10. What is the present value of these payments today? Assume an interest rate of 8%.

		$5,869.52
		$6,042.36
		$5,434.74
		$5,032.17

1. An investor expects to receive $3,000 each year for the next five years, with the first payment beginning at the end of the year. What is the present value of the these payments if the interest rate is expected to be 8% for years 1 and 2 and 5% thereafter?

		$15,354.03
		$13,456.28
		$14,216.70
		$12,354.03

Expert Solution

QUESTION 1

We need to calculate the future value of a 5 year annuity with 8% interest rate and $2000 payment. PV of annuity is represented mathematically as:

FV = $11,733.20

Question 2

In thsi question, we first need to calculate the PV of the 5 year annuity (of $3000) with discount rate 8% and then discount it further for 5 years to calculate value at time t = 0.

PV = $7,985.42. This is PV at time t = 5. We need to discount if for 5 more years to calculate the value todat (t = 0)

FV = PV * (1 + r)ⁿ

PV (at t=0) = 7,985.42/(1 + 8%)⁵

PV = $5,434.74 --> Answer

Question 3

Now, since interest rates are different for the annuity payment we won't use formula based approach.

We will break these into two annuities. One annuity that starts next year for 2 year and another that starts from 3rd year onwards.

PV (at t=0) of annuity (from Year 1 to Year2) = 3000/(1 + 0.08) + 3000/(1 + 0.08)² = $5,349.79

PV (at t=2) of annuity (from Year 3 to Year5) = 3000/(1 + 0.05) + 3000/(1 + 0.05)² + 3000/(1 + 0.05)³ = $8,169.74

Now PV of this second annuity needs to be discounted further to know value at t = 0. Interest rate for discounting would be 8%.

PV (at t=0) = 8,169.74/(1 + 0.08)² = 7,004.24

Hence total value of annuity today = $5,349.79 + $7,004.24 = $12,354.03

jeff jeffy answered 2 years ago

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