^[31] Amby Dextrous bought a grand piano and agreed to a series of monthly payments of $225 for 4 years starting the date of sale. The rate of interest is 13% compounded monthly.

a. Calculate the cash price.

b. How much will be paid over the term of its financing?

c. How much of the total payments will be interest?

 

^[32] Find the cash value of a three-year service contract for monthly payments of $1,600 paid at the beginning of each month. The value of money is 14% compounded monthly.

 

^[33] If an annuity with a present value of $50,000 has periodic payments at the beginning of each quarter for 10 years, find the size of the periodic payment. The rate of interest is 12% compounded quarterly.

 

^[34] An annuity whose present value is $50,000 is extinguished by payments of $650.00 made at the beginning of each month for 12 years.

a. Find the nominal rate of interest compounded monthly.

b. Calculate the effective rate.

 

^[35] Payments of $200 were made into a stock ownership plan at the beginning of each quarter for 15 years. They now have a net value of $50,000. What has been the nominal rate of return on the investment?

 

^[36] $100 is deposited into a retirement plan at the beginning of every month for 20 years. One month after the last deposit, money is withdrawn in equal monthly payments for 15 years. If interest is 8.5% compounded monthly, find the size of the monthly withdrawals.

 

^[37] If $75 is deposited into an education fund at the beginning of each month for 18 years and, one month after the final deposit, monthly withdrawals of $310.56 a month are made until the fund is exhausted, find the term of the annuity of withdrawals. Interest is 7.5% compounded monthly. (Try this problem both as an annuity due and an ordinary annuity.)

 

^[38] Find the present value of a deferred annuity whose periodic payment is $550 at the beginning of each year for 20 years, with the first payment following a two-year period of deferment. The interest rate is 3.6% compounded annually.

 

^[39] Find the present value of a deferred annuity whose periodic payment of $360.00 is made at the end of every semi-annual period for 18 years after a deferment period of six months. The interest rate is 10% compounded semiannually.

 

^[40] A deferred annuity has a present value of $15,000, and periodic payments are made at the beginning of each quarter for 10 years after a deferral period of 8 years. The rate of interest is 6% compounded quarterly. Find the size of the periodic payment.

 

^[41] Tri-City Holdings borrows $500,000 to fund the expansion of the firm into its eastern market region. If the loan is to be repaid by making equal payments at the end of each quarter for 8 years beginning after a deferral period of 2 years, find the size of the periodic payments. The interest rate is 11% compounded quarterly.

 

^[42] Find the present value of a perpetuity whose periodic payments of $4,000 are made at the end of each quarter. Interest is at 6.8% compounded quarterly.

 

^[43] An institute lecturer position in Math of Finance is being funded by a perpetual fund . The fund earns interest at I0% compounded annually and is to pay $60,000 at the end of each year, with the first payment two years from the date of the fund being set up. Find the size of initial funding required.

 

^[44] You want to have accumulated $4,000 for your European trip four years from now. If interest is 6.4% compounded quarterly, find the size of quarterly deposits required for 4 years if deposits are made:

a. at the beginning of each quarter.

b. at the end of each quarter.

 

^[45] A three-year car lease has a present value of $16,600. If money is worth 13.5% compounded monthly, find the equivalent monthly lease payments, payable in advance for 3 years.