Future Value of Single sum.
Mary deposits $5,000 today into a CD with 6% annual interest.
She wants to know how much money she will have in 4 years if the bank does the following.
(Hint: Rate and Nper change as the compounding period changes)
(a) annual compounding,
(b) semiannual compounding, and
(c) quarterly compounding.
2.
Present Value of a single sum.
John wants to have $10,000 in six years. He wants
to know how much to put away in bank today to get there. He can earn 4% annual interest.
Solve this problem if the bank offers
(a) annual compounding,
(b) semiannual compounding, and
(c) quarterly compounding.
3.
Future value of ordinary annuity.
(a) Lev will deposit $6,000 in an annuity each year (at the end of the year) for 10 years. How much will he have accumulated at the end of the 10th year? Assume 4 % annual interest.
(b) Lev will deposit $3,000 in an annuity every six months (at the end of the period) for the next 10 years. Assume 4% annual interest. How much will he have accumulated at the end of the 10th year?
4.
Present value of ordinary annuity and complete an amortization table.
a. Jonas will pay $5000 per year (at end of year) for loan that has an implicit rate of 9%. He will have paid off the loan at the end of the 4th year. What is the present value of the loan? (assume annual compounding)
b. show the amortization table. See Chapter 14, page 792 for an example of amortization table.
5.
Combo problem.
This requires you to solve for the present value of an ordinary annuity, and the present value of a single sum, then add them together. What is present value of the following cash flows?
(Hint: this is similar to bond pricing and you may want to read that part of the chapter again before completing this one).
· You will receive $10,000 at the end of each year for the next five years.
· In addition, at end of fifth year, you will also receive a lump sum payment of $100,000.
(a) The interest rate is 8%, annual
(b) The interest rate is 10% annual
6.
Find the payment of ordinary annuity.
Willie owes the government 800,000 in back taxes. The government will let him pay a fixed amount at the end of each year, as long as the sum is paid off in 5 years. The IRS requires 6% in interest (annual compounding) for this settlement. Find the payment.
7.
Mortgage question—find the payment and compare the financing alternatives:
You are taking out a $200,000 mortgage, you are considering 2 different terms (15 vs. 30 year). The 15 year rate is better, but you are not sure you can afford the payment. You are curious about the difference in the long term.
(a) find the payment, and find the total payments assuming 30 year mortgage, 5% annual rate. You do not need to do an amortization table. This will be a monthly payment so your Rate will be = (5% divided by 12 months) and your Nper will be = (30 years x 12 months). To find total cash paid, simply take (pmt x 12months x 30 years)
(b) find the payment assuming 15 year mortgage, 3.5% annual rate. Remember to adjust Nper and Rate for monthly payments. Then, pay total cash paid over the life of loan
find the difference in the total cash paid.