1. Today, your dream car costs $61,100. You feel that the price of the car will
ID: 2812958 • Letter: 1
Question
1. Today, your dream car costs $61,100. You feel that the price of the car will increase at an annual rate 2.1 percent. If you plan to wait 5 years to buy the car, how much will it cost at that time?
2. Beatrice invests $1,440 in an account that pays 3 percent simple interest. How much more could she have earned over a 4-year period if the interest had been compounded annually?
3. You have just received notification that you have won the $2.5 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you're around to collect), 65 years from now. What is the present value of your windfall if the appropriate discount rate is 11 percent?
Explanation / Answer
1.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
Hence
A=$61100*(1.021)^5
=$61100*1.109503586
=$67790.67(Approx).
2.
Simple interest=Principal*Interest rate*Time period
=(1440*3%*4)=$172.8
Hence total future value=Simple interest+Principal
=(1440+172.8)=$1612.8
For compound interest:
We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
A=$1440*(1.03)^4
=$1440*1.12550881
=$1620.73
Hence excess amount =$1620.73-$1612.8
=$7.93(Approx).
3.
Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period)
=$2,500,000/1.11^65
=$2,500,000*0.00113241699
=$2831.04(Approx).
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