Question

For each of the following annuities, calculate the annual cash flow. (Enter rounded answers as directed, but do not use rounded numbers in intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Cash Flow Present Value Interest Rate Years $ $ 32,500 11 % 6 $ 29,800 9 8 $ 161,000 14 11 $ 232,500 13 18

Answer 1

CONCEPT

1. The present value of an annuity is the current value of a set of cash flows in the future, given a specified rate of return or discount rate.

2. Present Value Of Annuity = CF*[(1-(1/(1+r)^n)) / r]

3. Cash Flow= PV*r/(1-(1/(1+r)^n)) Where, CF- Periodic Cash Flows, r - Interest rate (Periodic),n - Number of Periods for annual payments and n should be in years.

SOLUTION

(a) We have Present Value of Annuity = $32,500, Interest Rate = 11% and Period n = 6 years

Therefore, Annual Cash Flow = ($32500*11%)/(1-(1/(1+11%)^6)) = $7,682.24

(b) We have Present Value of Annuity = $29,800, Interest Rate = 9% and Period n = 8 years

Therefore, Annual Cash Flow = ($29800*9%)/(1-(1/(1+9%)^8)) = $5,384.10

(c) We have Present Value of Annuity = $161,000, Interest Rate = 14% and Period n = 11 years

Therefore, Annual Cash Flow = ($161000*14%)/(1-(1/(1+14%)^11)) = $29,526.48

(d) We have Present Value of Annuity = $232,500, Interest Rate = 13% and Period n = 18 years

Therefore, Annual Cash Flow = ($232500*13%)/(1-(1/(1+13%)^18)) = $33,991.70