Question

Applies TVM techniques using multiple compounding periods per year.

1.) 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?

2.) 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. Is more frequent compounding good for borrowers or for lenders and why?

3.) 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?

Answer 1

1.) Amount invested (P) = $100000

Annual rate of return (r) % = 12%

Time (t) = 10 years

Compounded times (n) = 4

Compunding formula = P (1 + r/n)^(nt)

where P is the initial principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods.

= 100000*(1+12%/4)^(4*10)

= $ 326,203.78

2.) No, it would not be better for the investment, if the number of times compounding is 1 then the amount would be $310,584.82 which is less if the compounding period is 4.

For borrowers = Frequent compounding is not better as it would lead to higher interests and borrower will have higher cost of capital.

For Lenders = Frequent Compounding is better as it would give lender a higher return for his amount.

3.) Time = 12 years

Interest = 6%

Compounded times = 12

Amount they want = $50000

we don't have Initial amount (P) this time, we have to find that,

$50000 = P*(1+6%/12)^(12*12)

After solving this,

P = $ 24,381.5