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07-MoreOnAnnuities.Rmd
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# More on Annuities
## 7.1 Annuities Due {-}
* You have contributed $3000 to your RRSP at the beginning of every three
months for the past 17 years. If the RRSP has earned 8.8% compounded quarterly, what is its value today?
* \$472,719.46 [Click here for full solution](https://youtu.be/K3yrDm7tl6g)
<p> </p>
* Carly purchased a refrigerator under a conditional sale contract that required 30 monthly payments of $70 with the first payment due on the purchase date. The interest rate on the outstanding balance was 15% compounded monthly.
a. What was the purchase price of the refrigerator?
b. How much interest did Carly pay during the entire contract?
* PV = \$1,764, Interest = \$336 [Click here for full solution](https://youtu.be/p2mRt2EBTwU)
<p> </p>
* For the past 25 years, Kiko has contributed $2500 to his RRSP at the beginning of every six months. The plan earned 8% compounded annually for the first 11 years and 7% compounded semiannually for the subsequent 14 years. What is the value of his RRSP today?
* $350,847.50 [Click here for full solution](https://youtu.be/VDduAGUwwms)
<p> </p>
* What is the current economic value of an annuity due consisting of 22 quarterly payments of \$700 if money is worth 6% compounded quarterly for the first three years, and 7% compounded quarterly thereafter?
* \$18,731.52 [Click here for full solution](https://youtu.be/VxBi7Z9PM-8)
<p> </p>
* A loan of \$35,000 is paid down to \$12,750 over the span of three years by making payments at the beginning of every month. If the current interest rate is 2.6% compounded annually, determine what the payment size should be.
* \$668.71 [Click here for full solution](https://youtu.be/pGpg34o3_Rw)
<p> </p>
* Sharon takes out a loan of \$45,000 and agrees to make payments of \$570 at the beginning of every other week. If the agreed upon rate is 2.5% compounded bi-weekly, how long will it take her to pay the loan down to \$12,000?
* N = 61, t = 2.35 years [Click here for full solution](https://youtu.be/JGW2CyZQAUE)
<p> </p>
## 7.2 Deferred Annuities {-}
* Liza has been able to transfer \$25,000 into an RRSP. She plans to
let the RRSP accumulate earnings at the rate of 4.5% compounded annually for 10 years, and then purchase a 15-year annuity making payments at the end of each quarter. What size of payment can she expect if the funds in the annuity earn 5.25% compounded quarterly?
* $938.98 [Click here for full solution](https://youtu.be/qvVwcHqFeTQ)
<p> </p>
* Twelve years ago, Frank rolled a \$21,000 retiring allowance into an RRSP that subsequently earned 11% compounded semiannually. Three years ago he transferred the funds to an RRIF. Since then, he has been withdrawing \$2500 at the end of each quarter. If the RRIF earns 7.5% compounded quarterly, how much longer can the withdrawals continue?
* N = 46, 8.5 years remaining [Click here for full solution](https://youtu.be/4rUnINokf4w)
<p> </p>
* The first quarterly payment of $850 in a five-year annuity will be paid 3.75 years from now. Based on a discount rate of 6.25% compounded monthly, what is present value of the payments today?
* \$11,651.43 [Click here for full solution](https://youtu.be/6tETuLJZYjk)
<p> </p>
* A \$45,000 loan bearing interest at 5% compounded quarterly was repaid, after a period of deferral, by quarterly payments of \$2,550 over 12 years. What was the time interval between the date of the loan and the first payment?
* N = 59, term = 14.75 years [Click here for full solution](https://youtu.be/RB_YRsIdrr0)
<p> </p>
* What amount must be invested today to provide for quarterly payments of $3500 at the end of every quarter for 15 years after a 5 year deferral period? Assume that the funds will earn 5% compounded semiannually.
* $115,165.91 [Click here for full solution](https://youtu.be/2E-Ku25v49E)
<p> </p>
* For how long (before the first withdrawal) must a \$25,000 investment earning 3.5% compounded semiannually be allowed to grow before it can provide 60 quarterly withdrawals of \$1200?
* N = 47, term = 23.5 years [Click here for full solution](https://youtu.be/HROuBEhhn44)
<p> </p>
## 7.3 Perpetuities {-}
* Determine the present value of a perpetuity that pays $350 at the beginning of each month. Assume interest is 3.5% compounded monthly.
* $120,350 [Click here for full solution](https://youtu.be/gcbeWhgFU1M)
<p> </p>
* If a perpetuity pays $200 at the end of each week, and the current rate of interest is 2.75% compounded monthly, what is the fair market value today of the perpetuity?
* $378,515 [Click here for full solution](https://youtu.be/wsgEJ8-_hEI)
<p> </p>
* A lottery has a grand prize of end-of-month payments of $150 for the rest of time. If the current interest rate is 5% compounded monthly, what is the fair market value today of winning this grand prize?
* $36,000 [Click here for full solution](https://youtu.be/Nzq2OwC2oWw)
<p> </p>
* Okanagan College would like to open a bank account that will pay one lucky student a $1500 bursary at the beginning of every year. If the current interest rate is 2% compounded biweekly, how much would the college have to deposit today into the bank account to ensure this perpetuity?
* $75,781.34 [Click here for full solution](https://youtu.be/fCGTURtMvKk)
<p> </p>
* The common shares of EDco are forecast to pay annual dividends of \$5 at the end of each of the next five years, followed by dividends of \$8 per year in perpetuity. What is the fair market value of the shares if the market requires an 8% annually compounded rate of return on shares having a similar degree of risk?
* \$88.02 [Click here for full solution](https://youtu.be/9aCiDE4raJ0)
<p> </p>
## 7.4 Constant Growth Annuities {-}
* Jessica intends to make RRSP contributions on January 1 of each year. She plans to contribute $2000 in the first year and increase the contribution by 3% every year thereafter. a. Rounded to the nearest dollar, how much will she have in her RRSP at the time of her 30th contribution if the
plan earns 8% compounded annually? b. What will be the amount of her last contribution?
* FV = $305,416, PMT = $4713.13 [Click here for full solution](https://youtu.be/YlYVsvwV8GU)
<p> </p>
* David is 30 years old and intends to accumulate $2.5 million in his RRSP by age 60. He expects his income and annual RRSP contributions to keep pace with inflation, which he assumes will be 2.5% per year. Rounded to the nearest dollar, what will be his initial contribution one year from now if he assumes the RRSP will earn 8% compounded annually?
* \$17,263 [Click here for full solution](https://youtu.be/s7-yTsPl1V4)
<p> </p>
## 7.5 Special Case Annuities {-}
* You purchase a car worth $25,000. You make a down payment of \$5000 and repay the rest with month end payments of \$350 with a final "buyout" of \$7500 due on the date of the final payment. How many payments do you make? Assume the rate of interest is 5.25% compounded quarterly.
* N = 44 [Click here for full solution](https://youtu.be/k2KcbSGJaeQ)
<p> </p>
* You make month end payments of \$250 into a retirement account for 30 years. At the end of each year, you contribute an additional \$2500 from your yearly bonus. How much will be in the account in 30 years? Assume the account earns 6% interest compounded semi-annually.
* \$448,424.57 [Click here for full solution](https://youtu.be/pEfam5pZZ50)
<p> </p>
* You wish to create a scholarship fund that pays \$10,000 to a recipient 3 times each year. You only have \$300,000 to invest today. If the fund into which you are investing earns 8% compounded quarterly, how long must you wait before you can award the first scholarship payment?
* N = 13, term = 3.25 years [Click here for full solution](https://youtu.be/0lcH8Hu7O6k)
<p> </p>
* A \$25,000 loan bearing interest at 9% compounded monthly was repaid, after a period of deferral, by monthly payments of \$430 for 10 years. What was the time interval between the date of the loan and the first payment?
* N = 42, term = 3.5 years [Click here for full solution](https://youtu.be/skbmiifC_kc)
<p> </p>