1-As you increase (decrease) the length of time involved, what happens to the pr
ID: 2613323 • Letter: 1
Question
1-As you increase (decrease) the length of time involved, what happens to the present value of an annuity? Explain why.
2-As you decrease (increase) the length of time involved, what happens to the future value of an annuity? Explain why.
3-What happens to the future value of an annuity if you increase (decrease) the interest rate? Explain why.
4-What happens to the present value of an annuity if you decrease (increase) the interest rate? Explain why.
5-What is the relationship between the future value (or present value) of an annuity due and an ordinary annuity expressed as an equation?
6-If you were an athlete negotiating a contract, would you want a big signing bonus payable immediately and smaller payments in the future, or would you want a small signing bonus payable immediately and larger payments in the future? Explain your answer.
7-Should lending laws be changed to require lenders to report EAR’s instead of APR’s? Why or why not?
8-On subsidized Stafford loans, a common source of financial aid for college students, interest does not begin to accrue until repayment begins. Who receives a bigger subsidy, a freshman or a senior? Explain.
9-What does continuous compounding mean?
10-In general, what is the relationship between a stated interest rate and an effective interest rate? Which is more relevant for financial decisions?
11-Which would be the LARGER dollar value, the future value of an ordinary annuity or the future value of an annuity due? Explain why.
12-Which would be the LARGER dollar value, the present value of an ordinary annuity or the present value of an annuity due? Explain why.
Explanation / Answer
Annuity = Annuity due * (1+i)
Thus it is better to report EAR also along with APR.
Annuity = Annuity Due * (1+r) where r is the interest rate.
Thus the Future Value of an annuity is higher than a Future Value of annuity due by the value 1+r (compounding factor).
Annuity = Annuity due *(1+r)
In the current case the annuity due should be further multiplied by a factor (1+r) ^n to arrive at Present value of annuity. Thus the Present Value of an annuity will be larger than the present value of annuity due
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