Question

What is the value today of a money machine that will pay $2,756.00 per year for 30.00 years? Assume the first payment is made 7.00 years from today and the interest rate is 6.00%.

What is the value today of a money machine that will pay $1,720.00 every six months for 29.00 years? Assume the first payment is made six months from today and the interest rate is 6.00%.

What is the value today of a money machine that will pay $1,060.00 per year for 10.00 years? Assume the first payment is made today and that there are 10.0 total payments. The interest rate is 7.00%.

Derek will deposit $3,988.00 per year for 19.00 years into an account that earns 6.00%. The first deposit is made next year. How much will be in the account 19.0 years from today?

Answer 1

1. Value of annuity 7 years from now using annuity formula = PMT*(1-(1+r)^-n)/r = 2756*(1-(1+6%)^-30)/6% = 37,935.87
PV of annuity today = 37,935.87/(1+6%)⁷ = 25,229.52

2. Rate half yearly = 6%/2 = 3%
Number of Periods = 29*2 = 58
PV of annuity today = PMT*(1-(1+r)^-n)/r = 1720*(1-(1+6%)^-58)/6% =27,690.25

3. PV of annuity due = (1+r)*PMT*(1-(1+r)^-n)/r = (1+6%)*1060*(1-(1+6%)^-58)/6% = 7801.13

4. FV of annuity = PMT*((1+r)ⁿ-1)/r = 3988*((1+6%)¹⁹-1)/6% = 134,634.85

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