Question

• Each question will be labeled as a calculator or formula question.
• For calculator problems , you are to label and input all the variables of interest: N, I/Y, PV, PMT, FV (and Begin mode if you switch). the unknown variable should be indicated by a ? symbol. Once solved, rewrite the variable identifier with the correct answer.
• For the formula problems, set up the problem and solve. Be sure to show each step for credit.
• Answer each question in BB in the space provided. Do NOT upload answers into BB.
• Round all $ problems to the nearest dollar.
• All rate problems must be carried at least 4 decimal places and left in % form.
• Work must be shown and all answers must be legible to receive credit. Partial credit is awarded.

4. Calculator problem:

You plan to invest in securities that pay 8.4%, compounded monthly. If you invest $15,000 today, how many years will it take for your investment to grow to $40,000.00?

5. Formula problem:

Suppose you decide to provide a charitable endowment that must pay $400,000 (assume an end of year lump sum payout). Your charity believes it can earn a return of 4.25% annually on the endowment. Using the formula approach, determine both of the following

a) How much would you would need to donate to fund this payout in perpetuity if the payout starts this year?

b) How much would you would need to donate to fund this payout in perpetuity if the payout starts ten years from now?

6. Formula problem:

Suppose you invest in a security that increases its return based on length of time held up to 30 years at which time it must be redeemed. You purchase the security for $25,000 today at a 4.8% annual rate that is compounded semiannually for 10 years. After 10 years the interest rate increases to a 6% rate compounded quarterly for the next 10 years. For the final 10 years, the rate goes up to 9% compounded monthly. What would your investment be worth at the end of the 30 years?

Thanks!

Answer 1

4)

Interest rate per month = 8.4%/12 = 0.7%

Using financial calculator

[N= ? ; I/Y = 8.4%/12 ; PV = 15000 ;PMT = 0 ; FV = 40000]

N Will come = 140.608 months

To convert to years we should divide by 12

Number of years = 140.608/12 = 11.72 years

5)

a)

Perpetuity = amount / interest rate

amount required to be donated = 400,000/4.25%

= $9,411,765

b)

If the payout starts 10 years from now we have to calculate present value of above donation amount.

Present value = Future value / (1+r)^n

Present value = 9411765/(1+4.25%)^10

Donation required = $6,207,410

6)

We use the same formula as above

Future value = present value*(1+r)^n

Balance after first 10 years:

Here compounded semi annually

Future value = 25000*(1+2.4%)^20 = 40,173.45

Balance after next 10 years:

Here it is compounded quarterly

Future value = 40173.45*(1+1.5%)^40 = 72,875.38

Balance after last 10 years:

Here it is monthly compounding

= 72,875.38*(1+0.75%)^120 = 178,644

investment value at the end of 10 years = $178 ,644