Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

TJ invested a retirement gratuity of $43 000.00 in an income averaging annuity paying 7% compounded monthly. He withdraws the money in equal monthly amounts over five years. If the first withdrawal is made nine months after the deposit, what is the size of each withdrawal?

The Saskatchewan Junior Achievers need to borrow to finance a project. Repayment of the loan involves payments of $8711.00 at the end of every three months for six years. No payments are to be made during the development period of three years. Interest is 9.24% compounded quarterly. a) How much did the Achievers borrow? b) What amount will be repaid? c) How much of that amount will be interest?

Anne-Marie received $445 000.00 from her mother's estate. She wants to set aside part of her inheritance for her retirement 12 years from now. At that time she would like to receive a pension supplement of $2600.00 at the end of each month for 15 years. If the first payment is due one month after her retirement and interest is 3.6% compounded monthly, how much must Anne-Marie set aside?

What semi-annual payment must be made into a fund at the beginning of every six months to accumulate to $4800.00 in ten years at 7% compounded semi-annually?

Carla Craig invested a retirement gratuity of $17 570.00 in an RRSP paying 6.5% compounded semi-annually for 11.5 years. At the end of 11.5 years, she rolled the RRSP balance over into an RRIF paying $1500.00 at the beginning of each month starting with the date of rollover. If interest on the RRIF is 9.5% compounded monthly, for how long will Carla receive monthly payments?

Mark contributed $270.00 at the end of every 3 months for 5.75 years into an RRSP earning 12.6% interest compounded quarterly. Four years after the last contribution he converted the RRSP into a RRIF that is to pay him quarterly payments for 29.5 years. If the first payment is due three months after the conversion into the RRIF and interest on the RRIF is 9.5% compounded quarterly, how much will Mark receive every 3 months?

Note: The calculations for this question were done using Excel's RATE function. A vacation property valued at $62 000.00 was bought for 40 payments of $2150.00 due at the beginning of every six months. What nominal rate of interest was charged?

What deposit made at the beginning of each month will accumulate to $36 000.00 at 5% compounded quarterly at the end of eight years?

Tricia bought a living-room suite on credit, signing an installment contract with a finance company that requires monthly payments of $167.25 for 4.5 years. The first payment is made on the date of signing and interest is 28.8% compounded monthly. a) What was the cash price? b) How much will Tricia pay in total? c) How much of what she pays will be interest?

Determine the accumulated value after 15 years of deposits of $500.00 made at the beginning of every 6 months and earning interest at 12% compounded monthly?

A property was purchased for quarterly payments of $1070.00 for 9 years. If the first payment was made on the date of purchase and interest is 5.57% compounded annually, what was the purchase price of the property?

Note: The calculations for this question were done using Excel's RATE function. What is the effective rate of interest charged on a lease valued at $17 040.00 if payments of $1180.00 are made at the beginning of each 3 months for four years?

What monthly lease payment due in advance should be charged for a tract of land valued at $135 000 if the agreed interest is 8.15% compounded semi-annually?

Mrs. Lavergne deposits $562.71 at the beginning of every three months. Starting three months after the last deposit, she intends to withdraw $587.00 every three months for 16 years. If interest is 8.14% compounded quarterly, for how long must Mrs. Lavergne make deposits?

Linda contributes $3000.00 at the beginning of every six months into an RRSP paying interest at 6% compounded semi-annually. a) How much will her RRSP deposits amount to in 15 years? b) How much of the amount will be interest?

You make six monthly deposits of $125 starting now. The interest rate is 6.36% compounded monthly. How much interest has been earned in total?

Kelly is saving $1600.00 at the beginning of each month. How soon can he retire if he wants to have a retirement fund of $345 000.00 and interest is 11.04% compounded monthly?

A lease requires payments of $1200.00 at the beginning of every quarter for ten years. If interest is 6% compounded monthly, calculate the value of the lease.

Compute the nominal annual rate of interest compounded monthly at which $1500.00 deposited at the beginning of every three months for ten years will amount to $90 000.00.

Equal payments are to be made at the end of each month for 12 years with interest at 9.66% compounded monthly. After the last payment, the fund is to be invested for 4 years at 6.82% compounded quarterly and have a maturity value of $27 600.00. What is the size of the monthly payment?