Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

The sum of $59 760.00 is invested at 9.5% compounded monthly for four years. After the four years, the balance in the fund is converted into an annuity due paying annually $15 240.00. If interest on the annuity is 9.57% compounded annually, what is the term of the annuity?

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.

Paul intends to retire in 15 years and would like to receive $8000.00 every 6 months for 20 years, starting on the date of his retirement. How much must he deposit in an account today if interest is 5% compounded semi-annually?

Calculate the present value of payments of $100.00 made at the beginning of each quarter for ten years if the interest is 6% compounded quarterly.

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 sum of $15 700.00 is invested at 6.48% compounded semi-annually for eight years. After the eight years, the balance in the fund is converted into an annuity paying equal payments at the end of every 6 months for 5.5 years. If interest on the annuity is 7.95% compounded monthly, what is the size of the equal payments?

At the beginning of every 6 months, $1280.00 is deposited for 8 years at 6.6% compounded monthly. After 8 years interest for the account is to be 9.66% compounded quarterly and the account is to be paid out by equal end-of-quarter quarterly payments over 6 years. What is the size of the quarterly payment?

Payments of $1000.00 are made into a fund at the beginning of every month for 10 years. If the fund earns interest at 12% compounded monthly, what will the balance in the fund at the end of the term?

Slick Sean contributes $500.00 at the beginning of each month into RRSP paying interest at 6.00% compounded semi-annually. What will be the accumulated balance in the RRSP at the end of 15 years?

Knowing that the education costs for her kids would be huge, Roberta puts lump sum money from her inheritance in a savings account paying an interest of 4.69% compounded semi-annually. If ordinary annuity payments of $1500.00 per month are to be paid out of the account at the end of the month for four years starting fifteen years from now, how much did Roberta deposit?

Note: The calculations for this question were done using Excel's RATE function. What is the nominal annual rate of interest charged quarterly on a lease valued at $2340.00 if payments of $240.00 are made at the beginning of every three months for 3.25 years?

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?

Bow Valley Credit Union entered a lease contract valued at $3100.00. The contract provides for payments at the beginning of each month for three years. If interest is 8.8% compounded quarterly, what is the size of the monthly payment?

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?

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?

National Research Council is considering the establishment in perpetuity of a Visiting Professor chair at UOIT. The ongoing cost will be $12 500 at the end of each month. If the money can earn 8% compounded monthly in perpetuity, what endowment is required to fund the position?

A contract valued at $81 500.00 requires payment of $3350.00 at the beginning of every six months. If interest is 6.5% compounded semi-annually, what is the term of the contract?

When Nancy died, she left $20 000 for her 13 year old grandson, Max, to be paid to him as an annual scholarship of $8000 at the beginning of each year, if he ends up in the university. The inheritance was invested in a scholarship fund for 5 years at 9% compounded annually. How long will the scholarship be paid, once Max enters the university?

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.