Fin 404 Case Study
FINC 404
Fall 2011
Assignment 1
Solution
1. I need your group names! Groups of 4 people please.
2. You can deposit $10,000 into an account paying 9% annual interest either today or exactly 10 years from today. How much better off will you be at the end of 40 years if you decide to make the initial deposit today rather than 10 years from today?
Solution
Deposit now: Deposit in 10 years:
FV40 = PV (1+k)40 FV30 = PV10 x (1+k)30
FV40 = $10,000 x (1.09)40 FV30 = PV10 x (1.09)30
FV40 = $314,090.00 (approx) FV30 = $132,680.00 (approx)
You would be better off by $181,410 ($314,090 - $132,680) by investing the $10,000 now instead of waiting for 10 years to make the investment.
3. Assume that you just won the state lottery. Your …show more content…
If payments are made at the beginning of each period the present value of each of the end-of-period cash flow streams will be multiplied by (1 + i) to get the present value of the beginning-of-period cash flows.
A $3,449.0 (1 + .12) = $3,862.50
B $123,616.8 (1 + .12) = $138,450.00
C $6,211.2 (1 + .12) = $$6,956.80
5. Janet Boyle intends to deposit $300 per year in a credit union for the next 10 years and the credit union pays an annual interest rate of 8%. a. Determine the future value that Janet will have at the end of 10 years given that end of year deposits are made and no interest is withdrawn if: 1) $300 is deposited annually and the credit union pays interest annually 2) $150 is deposited semiannually and the credit union pays interest semiannually 3) $75 is deposited quarterly and the credit union pays interest quarterly b. Use your finding in part (a) to discuss the effect of more frequent deposits and compounding of interest on the future value of the annuity.
a.
(1)Annual (2)Semiannual
FVA10 = $4,346.10 FVA10 = $4,466.70
(3) Quarterly
FVA10 = …show more content…
7. You have decided to endow your favorite university with a scholarship. It is expected to cost $6,000 per year to attend the university into perpetuity. You expect to give the university the endowment in 10 years and will accumulate it by making annual end of year deposits into an account. The rate of interest is expected to be 10% for all future time periods. a. How large must the endowment be? b. How much must you deposit at the end of each of the next 10 years to accumulate the required amount? Solution a. Present value of a perpetuity = PMT x (1 ( i) = $6,000 x (1 ( .10) = $6,000 x 10 = $60,000
b. PMT = $ 3,764.82 (rearrange FVA
Fall 2011
Assignment 1
Solution
1. I need your group names! Groups of 4 people please.
2. You can deposit $10,000 into an account paying 9% annual interest either today or exactly 10 years from today. How much better off will you be at the end of 40 years if you decide to make the initial deposit today rather than 10 years from today?
Solution
Deposit now: Deposit in 10 years:
FV40 = PV (1+k)40 FV30 = PV10 x (1+k)30
FV40 = $10,000 x (1.09)40 FV30 = PV10 x (1.09)30
FV40 = $314,090.00 (approx) FV30 = $132,680.00 (approx)
You would be better off by $181,410 ($314,090 - $132,680) by investing the $10,000 now instead of waiting for 10 years to make the investment.
3. Assume that you just won the state lottery. Your …show more content…
If payments are made at the beginning of each period the present value of each of the end-of-period cash flow streams will be multiplied by (1 + i) to get the present value of the beginning-of-period cash flows.
A $3,449.0 (1 + .12) = $3,862.50
B $123,616.8 (1 + .12) = $138,450.00
C $6,211.2 (1 + .12) = $$6,956.80
5. Janet Boyle intends to deposit $300 per year in a credit union for the next 10 years and the credit union pays an annual interest rate of 8%. a. Determine the future value that Janet will have at the end of 10 years given that end of year deposits are made and no interest is withdrawn if: 1) $300 is deposited annually and the credit union pays interest annually 2) $150 is deposited semiannually and the credit union pays interest semiannually 3) $75 is deposited quarterly and the credit union pays interest quarterly b. Use your finding in part (a) to discuss the effect of more frequent deposits and compounding of interest on the future value of the annuity.
a.
(1)Annual (2)Semiannual
FVA10 = $4,346.10 FVA10 = $4,466.70
(3) Quarterly
FVA10 = …show more content…
7. You have decided to endow your favorite university with a scholarship. It is expected to cost $6,000 per year to attend the university into perpetuity. You expect to give the university the endowment in 10 years and will accumulate it by making annual end of year deposits into an account. The rate of interest is expected to be 10% for all future time periods. a. How large must the endowment be? b. How much must you deposit at the end of each of the next 10 years to accumulate the required amount? Solution a. Present value of a perpetuity = PMT x (1 ( i) = $6,000 x (1 ( .10) = $6,000 x 10 = $60,000
b. PMT = $ 3,764.82 (rearrange FVA