[46] A Caribbean holiday tour package may be financed by making monthly payments of $300 at the beginning of each month for 2 years. Interest is 15% compounded monthly.
a. Find the purchase price now.
b. What will be the total paid in installments over the term?
c. How much interest will be paid over the term of the financing?
[47] A building will produce net monthly incomes of $2,000 at the beginning of each month indefinitely. What is the maximum purchase price if one can get 14% compounded monthly on one’s money?
[48] $400 is deposited into a retirement fund at the end of each quarter for 10 years, and interest is paid at a rate of 9.6% compounded quarterly.
a. Find the accumulated balance at the end of the 10 years.
b. How much of that balance is interest?
[49] A recreational property is purchased for $54,000 with a down payment of 10% and the balance secured by a mortgage, amortized by equal monthly payments over 20 years. Interest is 16% compounded monthly.
a. Find the size of the monthly payments.
b. Find the balance after 5 years.
c. How much will have been paid for the property in total over the 20-year term of the financing?
d. How much of the total payments will represent interest?
[50] An agreement for sale contract carries payments of $4,500 at the end of every six months for 10 years. How much should you be willing to pay for the contract if you require a return of 12.25% compounded monthly on your money?
[51] John Leisure purchased a small studio condominium at Whistler for $115,000. He paid $40,000 down and agreed to make equal payments at the end of every month for 25 years. The interest rate was 8.75% compounded semiannually. (see #36)
a. What size payment is John making each month?
b. After 10 years of payments, how much will John still owe?
c. How much will he have paid, in total, over the 25 years?
d. How much total interest will he have paid after 25 years of payments?
Simple Ordinary Annuities, Annuities Due, General Annuities
[52] Starting today, Mrs. Robinson will put $500 into her RRSP every month for 20 years. If her RRSP earns 6% compounded monthly, how much will she earn in interest over the 20 years?
[53] Mrs. Watson wants to save $52,450 for a down payment on a house. She will save $2,000 per quarter, starting today.
a. If her invested funds earn 6% compounded quarterly, how long will it take her to reach her goal?
b. How much interest will she earn during that time?
[54] You have just graduated from BCIT. You owe $15,238.98 in student loans. You will be charged 7% interest compounded monthly. You can afford to make monthly payments of $300 starting today.
a. How long (in years) will it take you to repay your student loans?
b. How much interest will you have paid?
[55] How long will it take to save $100,000 if you start saving $1,597 every 3 months, starting today? Assume an interest rate of 6%, compounded quarterly.
[56] You borrow $50,000 from the bank to consolidate your credit card debt and student loans. The bank charges you 12% interest, compounded monthly. The first payment is one month from now.
a. How long will it take to pay off the loan if you pay $504.25 per month?
b. What is the cost of financing?
c. How long will it take to pay off the loan if you pay only $500 per month?
[57] Mr. Eskanderian contributes $1,000 into his RRSP at the end of every quarter for 10 years. If his RRSP earns 10% compounded quarterly, how much interest will he earn in the 10 years?
Deferred Annuities
[58] Judith transfers $25,000 into an RRSP today. She plans to let the RRSP accumulate earnings at the rate of 8.75% compounded annually for exactly 10 years and then immediately purchase a 15-year annuity. The first withdrawal will start 3 months after she purchases the annuity. The annuity earns 9% compounded quarterly. What size of payment will she receive every 3 months?
[59] Katherine has recently received an inheritance. She wants to set aside part of the inheritance to put it into an RRSP to save for her retirement. She anticipates that she will need to receive $1,200 per month for 15 years, with the first withdrawal starting exactly 10 years from today. The invested funds will earn 7% compounded monthly for the entire 25 years. What amount must she contribute to her RRSP today?
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