P4–23 (LG-2/LG-3) 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? n= 30 r= 11.00% PVIFA= 30 periods, 11% Rate = 8.693793
Annuity= 20,000 / Present value = $173,876 = 20000 X 8.693793
Answer= $ 173,876 Retirement money required
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? n= 20 r= 9.00% FVIF= 20 periods, 9% = 5.604411
Amount required in 20 years = $ 173,876
Amount to be invested = $ 31,025
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.
If the interest in Part A went from .11 to .20 then we would need only $99,578.73.
In Part B it was .09 went to .15 including the interest from Part A was at .11 you would need $10,623.86
This is because higher compounding interest rates will provide more money, therefore you will not be required in today to get the same as tomorrow.
P4–46 (LG-6) 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.
a. PMT=$15,000 ÷ (PVIFA 14%, 3) PMT=$15,000 ÷ 2.322 PMT= $ 6,459.95 Answer: $ 6, 4459.97
b. Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.