1. If money is losing value at the rate of 2% annually because of inflation, how
ID: 2615638 • Letter: 1
Question
1. If money is losing value at the rate of 2% annually because of inflation, how long will it take a dollar, now assumed to be with 100 cents, to be worth 75 cents? Assume that inflation is continuously compounded.?
2. Suppose an investment of $7,000 earns 3% annual interest, compounded quarterly for a period of one year. When computing your income taxes, you find that the applicable federal rate is 28% of the interest and the applicable state rate is 7% of the interest. How much of the return on your investment do you keep??
make sure you use continuous compound interest in question 1 and for question 2, taxes are paid only on the interest !!!!!!!!
Explanation / Answer
1. Inflation rate = 2%
Present value of dollar = 100 cents
future value = 75 cents
Future value = Present value/ einflation * time
75 = 100/ e2%*t
e0.02*t = 100/75 = 4/3
0.02 * t = ln(4/3)
t = 14.3841
2. m = number of compounding , t= time
Interest recived = Amount * ( 1+ r/m)4t - Amount = 7000 ( 1 + 0.03/4)4 - 7000 = 212.37433
State tax = State tax rate * Interest = 7% * 212.37433 = 14.866
Federal tax = (Interest - State tax)* Federal tax rate = 197.50833 * 28%= 55.3023
Net interest income after taxes = 212.37433 - 14.866 - 55.3023 = 143.206
Return on investment = Net interest income after taxes / Investment = 143.206/7000 = 2.046%
Best of Luck. God Bless
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