2. Applies TVM techniques using multiple compounding periods per year. a. You ar
ID: 2820263 • Letter: 2
Question
2.
Applies TVM techniques using multiple compounding periods per year.
a.
You are saving for retirement and have the opportunity to invest in a security that pays a 12% annual rate of return, compounded quarterly. If you invest $100,000 in the security now how much will you have in your retirement account at the end of 10 years?
b.
Would it be better for your retirement account if the returns on the security were simply compounded once a year? (5 points) Explain why or why not. (15 points) Is more frequent compounding good for borrowers or for lenders and why? (30 points)
c.
Colin’s grandparents want to make a gift of $50,000 towards his college education fund in 12 years. How much money would they have to deposit today in an account that accrues interest monthly if the rate quoted by the bank is 6 percent?
2.
Applies TVM techniques using multiple compounding periods per year.
a.
You are saving for retirement and have the opportunity to invest in a security that pays a 12% annual rate of return, compounded quarterly. If you invest $100,000 in the security now how much will you have in your retirement account at the end of 10 years?
b.
Would it be better for your retirement account if the returns on the security were simply compounded once a year? (5 points) Explain why or why not. (15 points) Is more frequent compounding good for borrowers or for lenders and why? (30 points)
c.
Colin’s grandparents want to make a gift of $50,000 towards his college education fund in 12 years. How much money would they have to deposit today in an account that accrues interest monthly if the rate quoted by the bank is 6 percent?
Explanation / Answer
1-
Future value
FV =PV*(1+r)^n
100000*(1.03)^40
326203.78
2-
Future value
FV =PV*(1+r)^n
100000*(1.12)^10
310584.8208
it would not be better to you that returns are compounded once in a year instead of quarterly compounding because in yearly compounding only compounding would be once in a year while in case of quarterly compounding it would be 4 times in a year. It is better for more frequent compounding because this will increase the amount of interest earned on principal
3-
present value of retirement benefits at the time of retirement
Using Pmt function in MS excel
pmt(rate,nper,pv,fv,type) rate = 6%/12 = .5% nper =12*12 =144 pv =0 fv =50000 type = 1
PMT(.5%,144,0,50000,0)
($237.93)
1-
Future value
FV =PV*(1+r)^n
100000*(1.03)^40
326203.78
2-
Future value
FV =PV*(1+r)^n
100000*(1.12)^10
310584.8208
it would not be better to you that returns are compounded once in a year instead of quarterly compounding because in yearly compounding only compounding would be once in a year while in case of quarterly compounding it would be 4 times in a year. It is better for more frequent compounding because this will increase the amount of interest earned on principal
3-
present value of retirement benefits at the time of retirement
Using Pmt function in MS excel
pmt(rate,nper,pv,fv,type) rate = 6%/12 = .5% nper =12*12 =144 pv =0 fv =50000 type = 1
PMT(.5%,144,0,50000,0)
($237.93)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.