Exam 12: Annuities: Special Situations

A $30,000 loan bearing interest at 9% compounded monthly was repaid, after a period of deferral, by monthly payments of $425.10 for 10 years. What was the time interval between the date of the loan and the first payment?

Jack is 25 years old. He has deposited $1,000 into an RRSP fund, and plans to deposit $1,000 plus an additional 5% each year until he retires at age sixty-five. How much will Jack have in his RRSP account when he retires if money earns 4.75% compounded annually?

Mr. Larsen's will directed that $200,000 be invested to establish a perpetuity making payments at the end of each month to his wife for as long as she lives and subsequently to the Canadian Heart Foundation. What will the payments be if the funds can be invested to earn 5.4% compounded monthly?

As an employee benefit, a company has offered a fund of $750,000 for eligible children of employees to receive a scholarship of $2,500 per year for post-secondary education. If interest earns 4% compounded annually, how many scholarships can be provided per year?

A finance company paid a merchant $3,975 for a conditional sale contract after discounting it to yield 18% compounded monthly. If the contract is for 20 monthly payments of $256.96 following a payment-free period, what is the time interval between the date of sale and the first payment?

Mary needs a pension that will pay her $12,000 one year from now and annual payments for 24 more years that are each 5% larger than the previous year. If the funds in her Retirement Fund earn 7.5% compounded annually, how much money must she have there now?

Using an inheritance he recently received, Sam wants to purchase a deferred annuity that will pay $5,000 every three months between age 60 (when he plans to retire) and age 65 (when his permanent pension will begin). The first payment will be received three months after he reaches 60, and the last payment will be received on his 65^th birthday. If Sam's current age is 50 years and 6 months and the invested funds will earn 4.4% compounded quarterly, what amount must he invest in the deferred annuity?

A retiree of the local college has asked that any money collected for a retirement gift be used to set up a perpetuity scholarship fund for a third-year student in the School of Business. A total of $3750 was collected. If interest earns 4% compounded annually, what will be the amount of the yearly scholarship?

The Bay is offering "no money down, and no payments for a year." The total cost of a purchase of electronic equipment is $3500 including taxes. What monthly payment is required to pay off this debt in two years, if payments start in one year, and the Bay charges interest at 2% per month? What is the amount of interest that the purchaser pays overall?

Baba Lou plans to retire in 20 years. At that point, he plans to collect payments at the end of every six months that are 2% larger than the previous payment, and this is to continue for 30 years. The first payment will be $16,500. His retirement plan is expected to earn 7% compounded semi-annually after he retires and 10% compounded annually before he retires. What single investment should he make now to fund the whole retirement plan?

Harold, just turned 27, wants to accumulate an amount in his RRSP at age 60 that will have the purchasing power of $300,000 in current dollars. What annual contributions on his 28^th through 60^th birthdays are required to meet this goal if the RRSP earns 8.5% compounded annually and the rate of inflation is 2.5% per year?

What amount can be paid at the end of every month in perpetuity from an endowment of $350,000 which is earning 5.4% compounded monthly?

What is the economic value today of 24 monthly payments of $500 with the first payment occurring 10 months from today? Assume that money can earn 12% compounded monthly.

Marika wants to have $500,000 in her RRSP account in 40 years. Money currently earns 4.25% compounded annually, and Marika plans to make contributions to her RRSP account at the end of each year increased each time by 3% to adjust for inflation. What will be Marika's initial contribution?

Barklay has $782,490 in his Retirement Saving Plan and he wants to start receiving income at the end of every three months for the next 22 years. The funds earn 7% compounded quarterly and he wants each payment that he receives to be 1.5% larger than the previous one. How much will the first payment be three months from now?

How much will it cost to purchase a 20-year indexed annuity in which the end of quarter payments start at $6,000 and grow by 0.5% every quarter? Assume that the money used to purchase the annuity earns 8% compounded quarterly.

Randall wants to accumulate $750,000 in his RRSP by the end of his 30-year working career. What should be his initial year-end contribution if he intends to increase the contribution by 3% every year and the RRSP earns 5.25% compounded annually?

The Willie P. Stanton Trust Fund is to pay, $5,000 at the end of every year to the student-athlete voted most deserving based on his or her dedication to the ideals of good citizenship. The Trust Fund earns 7.4% compounded semi-annually. What is the present value of this perpetuity?

Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

If an endowment fund of $2,327,000 is to be used to pay out grants of $175,000 at the end of every year in perpetuity what effective rate of interest must the funds earn?