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1
1. Suppose you earned a $300,000 bonus this year and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?
2. Suppose you just won the state lottery, and you have a choice between receiving $3,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.
3. What's the present value of $19,000 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?
4. American Express and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 25.00%, with interest paid monthly, what is the card's EFF%?
5. John Smith borrowed $230,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would John have to pay in a 30-day month?
Expert Solution
1). We can calculate the annual withdrawal by using the following formula in excel:-
=pmt(rate,nper,-pv,fv)
Here,
Pmt = Annual withdrawal
Rate = 8.25%
Nper = 20 periods
PV = $300,000
FV = $0
Substituting the values in formula:
= pmt(8.25%,20,-300000,0)
= $31,126.31
2). We can calculate the rate of return by using the following formula in excel:-
=rate(nper,pmt,-pv,fv)
Here,
Rate = Rate of return
Nper = 20 periods
Pmt = $250,000
PV = $3,550,000
FV = $0
Substituting the values in formula:
= rate(20,250000,-3550000,0)
= 3.51%
3). We can calculate the present value by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Present value
Rate = 4.5% (semiannual)
Nper = 5*2 = 10 periods (semiannual)
Pmt = $0
FV = $19,000
Substituting the values in formula:
= -pv(4.5%,10,0,19000)
= $12,234.63
4). computation of the card's EFF:-
EFF = (1+APR/n)^n-1
= (1+25%/12)^12-1
= 1.2807 - 1
= 28.07%
5). Computation of the simple interest:-
Simple interest = Principal * Rate * Time
= $230,000 * 7.25% * 30 / 360
= $1,389.58
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