Annuities and Perpetuities

What is the term for a consistent series of cash flows occurring at regular intervals over a defined timeframe?

Assuming all other factors remain constant, which of the following changes would lead to an increase in the present value of an annuity?

If both an ordinary annuity and an annuity due have $500 annual cash flows for 20 years and share the same interest rate, which has the higher present value?

What term describes a consistent stream of equal cash payments that continues indefinitely?

How is the present value of a perpetuity calculated?

Given that a perpetuity and an annuity have the same payment amounts and interest rate, how will the present value of the perpetuity compare to that of the annuity?

An annuity pays $950 each year. Payments start 13 years from today and end 27 years from today. How many payments are made?

You receive an insurance settlement that pays $8,000 per year, starting at the beginning of year 3 and ending 18 years from today. How many payments will you receive?

What is the present value of a five-period annuity of $3,000 paid annually with a 12% interest rate, where the first payment is made one year from today?

An annuity due will make eight annual payments of $4,000. If the discount rate is 5%, what is its present value?

If you invest $2,000 at the end of each of the next 40 years and earn 9% per year, how much will you accumulate?

An ordinary annuity makes seven annual payments of $1,342. If the present value of these payments is $7,585.65, what is the discount rate?

What is the monthly payment on a $675,000 30-year home mortgage with a 3.6% APR, assuming a $40,000 down payment and payments at the end of each month?

What is the present value of a $5 million prize paid in 20 equal yearly installments, beginning today, with a 7% discount rate?

The present value of an ordinary annuity paying $128 per year is $5,682 at a 9.5% rate. Approximately how much would its value change if it were an annuity due?

An ordinary annuity has a present value of $24,000, while an otherwise identical annuity due has a present value of $25,000. What discount rate is implied?

A perpetuity pays $1,200 annually at the end of each year. To earn a 7.5% annual return, how much should you pay for it today?

An ordinary perpetuity sells for $14,500 and has a 4.48% return. What will the perpetuity pay annually?

You're considering buying a perpetuity that makes annual payments of $7,500 at the end of each year, starting one year from today. If the asking price is $56,000, what is the implied interest rate?

A perpetuity pays $5,000 per year, with payments starting today, offering a 12.5% return. What is its present value?

What is the present value of a ten-year annuity of $1,500 per year, with the first payment five years from today, assuming a 6% discount rate?

The present value of a five-period ordinary annuity is $4,600. With an 8.5% discount rate, what would the annual payment be if the first payment occurred nine years from today?

A perpetuity pays $840 at the end of each year, with the first payment seven years from today, and a 3.36% discount rate. What is the present value of the perpetuity?

An ordinary perpetuity pays $100 per year. At a 6.4% interest rate, what would an eight-year annuity due payment need to be to have the same present value as the perpetuity?

What is the present value of a growing perpetuity with payments of $1,080 that increase annually at 2.3%, assuming a 7.7% cost of capital?

The present value of a deferred growing perpetuity is $50,000, with an 8% rate of return and a 2.5% payment growth rate. If the first payment occurs six years from today, what is the amount of that payment?

Scotty's real estate agent states homes in his price range involve payments of $1,850.93 monthly for 30 years at 4.2% APR. Assuming end of period payments, what would the payment be on a 15-year mortgage?

DJ wants to live on $100,000 per year in retirement, increasing with inflation at 3.6% annually. With a 7.6% investment return, how much money must DJ have when he retires (first payment one year after retirement)?

Bill will buy his friend's horse, Thundercloud, with nine equal monthly payments starting two months from today. If the horse is valued at $7,465 and the cost of capital is 10.2%, what will Bill's payment be?

TCB Motorcycles offers $522.59 monthly payments for 48 months on a $25,000 bike after a $4,000 down payment. What is the loan's APR, with end-of-month payments?

The Hound Dog Diner wants to establish a growing Employee of the Year award with an initial prize of $2,500, growing 3% annually. How much does the company need to invest if they invest at 8%, and the first prize begins today?

Today, Colonel Tom got a bank loan to open a Parker's Chicken franchise. The loan requires annual payments of $56,475.96 with the first payment being made two years from today and the last payment being made 35 years from today. If the interest rate on the loan is 5.8%, how much did Tom borrow from the bank?

Gladys invests $1,000 at the end of each year for eight years, starting one year from today. It pays 12% annually for the first four years and 8% for the last four. What will her account balance be at the end of eight years?

Vernon wants to buy a gold ring for his wife. Option 1 is to buy the ring today for $40,000 cash. Option 2 requires a down payment and then a monthly payment of $963.81 for 36 months (first payment one month from today). If the APR is 6.6%, what is the required down payment using option 2?

James wants to retire 20 years from today and then start withdrawing $120,000/year for each of the next 25 years. At a 12% interest rate, how much does he need to save at the end of each of the next 20 years to achieve his goal?

Grace has two investment options: $5,000 per year starting at age 25 or $10,000 per year starting at age 35. Last deposit for either is age 64, with a 9.5% interest rate. How much more/less would Grace have at age 64 investing in Option 2 vs Option 1?

The Heartbreak Hotel bought a property for $500,000, financing it with a 30-year, 4.9% APR annual payment loan. When half the mortgage is paid off (remaining principal balance is $250,000), how many payments remain?

Sun Records needs to buy $38,000 recording equipment in five years. They've saved $17,000 and plan to deposit $1,800/year. What interest rate does Sun need to earn?

Sam will retire in 10 years and wants to throw a huge party funded by a $1,500 deposit made today and equal annual deposits of $500 made two to ten years from today, and also depositing a lump sum of $1,000 five years from today. How much money will he have if he can earn 6.5%?

The US president earns $400,000/year while in office and a $226,300 annual pension for life after leaving office, paid at each year's end. Assuming an 8-year term and 7% interest, what is the present value of this compensation plan?