Padayappa has now retired after 40 years of employment. He just made an annual d
ID: 2722612 • Letter: P
Question
Padayappa has now retired after 40 years of employment. He just made an annual deposit to his investment portfolio and realized he has $1,550,000 (not counting home, cars, furniture, etc.). His money has been earning 7 percent per year, and inflation has been running 4 percent per year over the past 40 years. What equal amount of money did he put into his investment at the end of each year? $ Carry all interim calculations to 5 decimal places and then round your final answer to the nearest dollar. The tolerance is plusminus 5. What is the buying power of his $1,550,000 in terms of a base 40 years ago? $ Carry all interim calculations to 5 decimal places and then round your final answer to the nearest dollar. The tolerance is plusminus 50. If he could buy a TV 40 years ago for $250, what would a comparable one cost today if the consumer electronics inflation rate is -3 percent? $ Carry all interim calculations to 5 decimal places and then round your final answer to the nearest dollar. The tolerance is plusminus 1.Explanation / Answer
1)It is based on the concept of time value of money wherein he made an annual deposit in his investment fund for 40 years and now we know the lump sum value accumulated at the end of the period.
We need to calculate the annual deposit made for 40 years.The deposit earned an interest of 7% p.a. and inflation rate is 3%,so the real rate of interest,r=7=3%
r=inflation adjusted interest rate or real interest rate=7-4=3
Future value of annuity=9C * (1+r) ^n-1))/r
1550000=(C* ((1+.03)^40-1))/.03
C=20556.69
If $ 20556.69 is invested each year at an interest rate of 7% and prevailing inflation rate of 4% , it will grow to amount 1550000 at the end of 40 years.
2) Here ,we need to find the present value of 155000 40 years ago. So we will discount it by the inflation adjusted interest rate to find its buying power 40 years before.
Present value of money=Future value/(1+r)^n
Future value=1550000
r =3%
n=40
Present value=475163.10
Buying power 40 years before=475163.10
3)
Here we need to find the future value of $250 after 40 years given the inflation rate of 3%.
Investment Results
Initial Investment (PV) $250.00
Effects of Inflation on PV $76.64
Future Value (FV) $3,743.61
FV Adjusted for Inflation $1,147.63
Interpretation
$250.00 40 years before has a value of $1,147.63 in today's dollars.
Your account statement will read $3,743.61 after 40 years however, adjusted for the effects of inflation ,it will have a value of $1,147.63 in today's dollars for $250 deposited 40 years before.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.