Finance for Decision Making
January 30, 2012
Chapter 4: Problem 4-23 – Personal Finance Problem Funding your retirement - You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $20,000 at the end of each year for the 30 years between retirement and death (a psychic told you would die exactly 30 years after you retire). You know that you will be able to earn 11% per year during the 30-year retirement period.
a. How large a fund will you need when you retire in 20 years to provide the 30-year, $20,000 retirement annuity?
$173,880 will be required to retire in 20 years to provide the 30-year, $20,000 retirement annuity. Calculated as follows: According to Gitman (2009), present value (annuity): = (, ) PVA = PMT x (PVIFA11%, 30)
PVA = $20,000 x (8.694)
PVA = $173,880
b. How much will you need today as a single amount to provide the fund calculated in part “a” if you earn only 9% per year during the 20 years preceding retirement?
$30,950.64 would be needed today to provide $173,880 assuming only 9% is earned per year during the 20 years preceding retirement. According to Gitman (2009), present value (single amount): = (, ) PV = FV x (PVIF9%,20)
PV = $173,880 x (0.178)
c. What effect would an increase in the rate you can earn both during and prior to retirement have on the values found in parts “a” and “b”? Explain.
The effect an increase in the rate you can earn both during and prior to retirement would decrease the values in parts a and b. A smaller amount would be required in 20 years, and a smaller amount would need to be saved.
Chapter 4: Problem 4-32 – Personal Finance Problem Funding budget shortfalls - As part of your personal budgeting process, you have determined that in each of the next 5 years you will have budget shortfalls. In other words, you will need the amounts shown in the following table at the end of the given year to balance your budget—that is, to make inflows equal outflows. You expect to be able to earn 8% on your investments during the next 5 years and wish to fund the budget shortfalls over the next 5 years with a single amount.
a. How large must the single deposit today into an account paying 8% annual interest be to provide for full coverage of the anticipated budget shortfalls?
Based on the calculations below, a single deposit of $22,215 is required to provide for full coverage of the anticipated budget shortfalls.
Year| Budget Shortfall| | PVIF| | Present Value|
1| $ 5,000| x| 0.926| =| $4,630|
2| $ 4,000| x| 0.857| =| $3,428|
3| $ 6,000| x| 0.794| =| $4,764|
4| $10,000| x| 0.735| =| $7,350|
5| $ 3,000| x| 0.681| =| $2,043|
| | | | | $22,215|
b. What effect would an increase in your earnings rate have on the amount calculated in part “a”? Explain
An increase in earnings rate would decrease the amount calculated in part a. A higher rate generates a higher interest and allows a decrease in the initial investment.
Chapter 4: Problem 4-46 – Personal Finance Problem
Loan amortization schedule - Joan Messineo borrowed $15,000 at a 14% annual rate of interest to be repaid over 3 years. The loan is amortized into three equal, annual, end-of-year payments.
a. Calculate the annual, end-of-year loan payment.
PMT = $15,000 (PVIFA14%, 3)
PMT = $15,000 / 2.322
PMT = $6,459.95
b. Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.
Year| Beginning Balance| Payment| Principal| Interest| Ending Balance| 1| $15,000.00| $6,459.95| $4,359.95| $2,100.00| $10,640.05| 2| $10,640.05| $6,459.95| $4,970.34| $1,489.61| $ 5,669.71| 3| $ 5,669.71| $6,459.95| $5,666.19| $ 793.76| $ 0.00|