Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

Payments on a six-year lease valued at $12 975.00 are to be made at the beginning of each month during the last 3 years of the lease. If interest is 9% compounded monthly, what is the size of the monthly payments?

A sum of money is deposited at the beginning of each year for 3 years at 12% compounded annually. After the last deposit interest for the account is to be 8.24% compounded quarterly and the account is to be paid out by payments of $370.00, made at the beginning of each quarter for nine years. What is the size of the annual deposit?

Enermax offers to acquire a right-of-way from a property owner who receives annual lease payments of $3725.00 due in advance. What is a fair offer if money is worth 6.5% compounded quarterly?

Gibran bought a boat valued at $110 194.00 on the installment plan. He made equal semi-annual payments for 6 years. If the first payment is due on the date of purchase and interest is 7.5% compounded semi-annually, what is the size of the semi-annual payments?

Starting three months after her grandchild Crystal's birth, Mrs. Robinson made deposits of $63.25 into a trust fund every three months until Crystal was 19 years old. The trust fund provides for equal withdrawals at the end of each quarter for 5 years beginning three months after the last deposit. If interest is 8.24% compounded quarterly, how much will Crystal receive every three months?

Monica would like to receive $3760.00 at the end of every six months for 8 years after her retirement. If she retires ten years from now and interest is 6.5% compounded semi-annually, how much must she deposit into an account every six months starting now?

How many months will it take to accumulate $17897.20 at 5.87% compounded semi-annually, if $1140.00 is deposited in an account at the beginning of every 6 months?

What is the accumulated value after 15 years of monthly deposits of $500.00 earning interest at 8% compounded semi-annually if the deposits are made a) at the end of each month? b) at the beginning of each month?

Hector makes payments of $2000.00 into an RRSP at the beginning of every six months starting today for 33 years. If the interest rate is 8% compounded semi-annually, calculate the accumulated value.

What is the discounted value of deposits of $570.00 made at the beginning of every three months for 8.25 years if money is worth 8.4% compounded quarterly?

How much does a depositor have to save at the beginning of every three months for 15 years to accumulate $200000.00 if interest is 4% compounded quarterly?

An investment in a lease offers returns of $3713 per month due at the beginning of each month for 4.5 years. What investment is justified if the returns are deferred for two years and the interest required is 6.12% compounded monthly?

An annuity provides payments of $4580.00 at the end of every three months. The annuity is bought for $53 500.00 and payments are deferred for 10 years. If interest is 9.72% compounded monthly, for how long will payments be received?

Jack Chen makes deposits of $415.00 at the beginning of every three months. Interest earned by the deposits is 4.12% compounded quarterly. a) What will the balance in Jack's account be after eight years? b) How much of the balance will Jack have contributed? c) How much of the balance is interest?

Beverley intends to retire in 7.25 years and would like to receive $2700.00 every month for 12.25 years starting on the date of her retirement. How much must she deposit in an account today if interest is 11.36% compounded annually?

A sum of money is deposited at the end of every 6 months for 9.5 years at 8% compounded semi-annually. After the last deposit, interest for the account is to be 4.5% compounded quarterly and the account is to be paid out by making payments of $4360.00 at the end of each month over 7.75 years. What is the size of the semi-annual deposit?

A man received a separation payment of $98000.00 at age 56. He invested that sum of money at 8.5% compounded semi-annually until he was 65. At that time he converted the existing balance into an ordinary annuity paying $6150.00 every 6 months, with interest at 5% compounded semi-annually. How many payments will be made?

Fraser deposits $790.00 at the beginning of every three months. He wants to build up his account so that he can withdraw $1550.00 every three months starting three months after the last deposit. If he wants to make the withdrawals for 16 years and interest is 6.64% compounded quarterly, for how long must Fraser make the quarterly deposits?

Determine the accumulated value after 15 years of deposits of $9000.00 made at the beginning of every three months and earning interest at 8% compounded quarterly.

A fund to provide an annual scholarship of $5700.00 is to be set up. If the first payment is due in three years and interest is 6.4% compounded quarterly, what sum of money must be deposited in the scholarship fund today?