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1) Assume that you have to pay rent as a growing perpetuity
1) Assume that you have to pay rent as a growing perpetuity. The first payment will occur in a year and will be $24,000. Each year after that, you will receive a payment on the anniversary of the last payment that is 4.5% larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is 8% per year.
a. What is today's value of the rent? b. What is the value of the rent immediately after the first payment is made?
2) You are thinking about buying a savings bond. The bond costs $500 today and will mature in 10 years with a value of $1000. What annual interest rate will the bond earn?
3) You have an investment opportunity that requires an initial investment of $1100 today and will pay $1300 in one year. What is the rate of return of this opportunity?
4) Suppose you currently have $47,000 in your savings account, and your bank pays interest at a rate of 0.175% per month. If you make no further deposits or withdrawals, how much will you have in the account in five years?
Expert Solution
1-a). Computation of the value of today:-
Value of today = Cash flow / (Required return - Growth rate)
= $24,000 / (8% - 4.50%)
= $24,000 / 3.50%
= $685,714.29
b). Computation of the value of 1 year from now:-
Value of 1 year from now = CF*(1+growth rate) / (Required return - Growth rate)
= $24,000*(1+4.50%)/(8% - 4.50%)
= $25,080 / 3.50%
= $716,571.43
2). We can calculate the annual interest rate by using the following formula in excel:-
=rate(nper,pmt,-pv,fv)
Here,
Rate = Annual interest rate
Nper = 10 periods
Pmt = $0
PV = $500
FV = $1,000
Substituting the values in formula:
= rate(10,0,-500,1000)
= 7.18%
3). Computation of the rate of return:-
Rate of return = (Ending value - Beginning value) / Beginning value
= ($1,300 - $1,100) / $1,100
= $200 / $1,100
= 18.18%
4). Computation of the future value:-
FV = PV*(1+rate)6n
Here,
n = 5*12 = 60 periods (monthly)
FV = $47,000*(1+0.175%)^60
= $47,000*1.11061
= $52,198.61
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