M114/05-CompoundInterest.Rmd at main · TheElementsMath/M114 · GitHub

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#  Compound Interest

##  5.2 Present and Future Values {-}

*  I invest \$15000 for 25 years.  How much money do I have if the rate of interest is 6% compounded annually, 6% compounded semiannually, 6% compounded quarterly and 6% compounded monthly?
    *  \$64,378.06, \$65,758.59, \$66,480.68, and \$66,974.55  [Click here for full solution](https://youtu.be/1naYhKBUN-E)
<p>&nbsp;</p>


*  What is the maturity value of a $14,000 loan for 18 months at 5.2% compounded quarterly?
How much interest is charged on the loan?
    *  maturity value \$15,128.11, interest \$1128.11  [Click here for full solution](https://youtu.be/zO_44LiJfKM)
<p>&nbsp;</p>


*  In 1981, you could earn 17.5% compounded annually on a five-year term deposit. Since then, the interest rate offered on five-year term deposits dropped as low as 2.0% compounded annually in 2013. On a $10,000 deposit for a term of five years, how much more would you have earned at the high interest rate than at the low rate?
    *  \$11,356.16  [Click here for full solution](https://youtu.be/VbjDxKdtpms)
<p>&nbsp;</p>


*  A loan of \$7000 at 7.5% compounded monthly requires three payments of \$1500 at 6, 12, and
18 months after the date of the loan, and a final payment of the full balance after two years.
What is the amount of the final payment?
    *  \$3277.45  [Click here for full solution](https://youtu.be/M9I7h4DKWxQ)
<p>&nbsp;</p>


*  What amount today is economically equivalent to \$18,000 paid 18 months from now, if money
is worth 5% compounded monthly?
    *  \$16,701.99  [Click here for full solution](https://youtu.be/laulauAcX34)
<p>&nbsp;</p>


*  You owe \$65,000 payable three years from now. What alternative amount should your creditor be willing to accept today if she can earn 4.75% compounded monthly?
    *  \$56,383.05  [Click here for full solution](https://youtu.be/AGEIRcuFdM0)
<p>&nbsp;</p>


*  How much must a 25-year-old individual invest five years from now to have the same maturity value at age 55 as an immediate investment of $1000? Assume that both investments earn 7% compounded annually.
    *  \$1402.55  [Click here for full solution](https://youtu.be/PAjqOck5pG0)
<p>&nbsp;</p>


*  If the total interest earned on an investment at 6.75% compounded semiannually for 8.5 years
was $17,438.19, what was the original investment?
    *  \$23,000  [Click here for full solution](https://youtu.be/vFZjat5S_pY)
<p>&nbsp;</p>


##  5.3  Calculating the Periodic Interest Rate and Number of Compounding Periods {-}


*  An initial investment of \$1900 is worth \$2400 after two years and nine months. What quarterly compounded nominal rate of return did the investment earn?
    * 8.59% per year compounded quarterly.  [Click here for full solution](https://youtu.be/ursDj7Csxvc)
<p>&nbsp;</p>


*  The maturity value of a \$10,000 four-year compound interest GIC was \$11,647.82. What
quarterly compounded rate of interest did it earn?
    *  3.83% per year compounded quarterly.  [Click here for full solution](https://youtu.be/YHEUee-vdHQ)
<p>&nbsp;</p>


*  A five-year promissory note for \$5500 plus interest at 6.75% compounded semiannually was sold 18 months before maturity for \$6500. What monthly compounded nominal rate of return will the buyer realize on the investment?
    *  11.04%  [Click here for full solution](https://youtu.be/L8GIkawEmgA)
<p>&nbsp;</p>


*  A number of years ago, your client invested \$16,000 at a rate of return of 9% compounded annually. If the investment is currently worth \$20,968.25, for how long has she held the investment?  (Do not round your answer).
    *  3.138 years  [Click here for full solution](https://youtu.be/-IpQf5cbgKQ)
<p>&nbsp;</p>


*  If money is worth 8% compounded quarterly, how long before a scheduled payment of \$6000 will \$5000 be an equivalent payment?
    *  2.5 years  [Click here for full solution](https://youtu.be/0yoaQygnxVs)
<p>&nbsp;</p>


##  5.4  Equivalent Payments and Payment Streams {-}

*  A payment stream consists of \$1950 due today and \$3500 due in 18 months.  These payments will be replaced by an economically equivalent stream comprised of an undetermined payment due in 10 months and a payment of \$3000 due in 24 months. Calculate the unknown replacement payment if money is worth 8% compounded monthly.
    *  \$2669.26  [Click here for full solution](https://youtu.be/s7hgkpi41dA)
<p>&nbsp;</p>


*  Payments of \$1850 due two years ago and \$1550 due six months ago have not been made.  The proposed alternative is two equal payments, three months and nine months from now, that will put the payee in an equivalent economic position allowing that money can earn 4.3% compounded quarterly. What is the amount of each of these payments?
    *  $1838.15  [Click here for full solution](https://youtu.be/CfhIoqV-ujM)
<p>&nbsp;</p>


*  The scheduled payment stream consists of \$6000 due today and \$12,000 due in five years.  It is proposed to replace this stream by an economically equivalent stream comprised of three equal payments due one, three, and five years from now. Determine the size of each payment if money is worth 4% compounded annually.
    *  \$5935.77  [Click here for full solution](https://youtu.be/2y_5Qe8dVVI)
<p>&nbsp;</p>


*  Payments of \$10,000 due 15 months ago and \$7000 due in six months are to be replaced by a
payment of \$4000 today, a second payment in nine months, and a third payment, three times
as large as the second, in 1.5 years. What should the last two payments be if money is worth
6.4% compounded quarterly?
    *  First payment = \$3696.67, second payment = \$11,090.01.  [Click here for full solution](https://youtu.be/a9x41uJoY7o)
<p>&nbsp;</p>


*  Three years ago, Ayia loaned \$2500 to John. The principal with interest at 8% compounded semiannually is to be repaid four years from the date of the loan. Eighteen months ago, John borrowed another \$1500 for 2.5 years at 7% compounded semiannually.  John is now proposing to settle both debts with two equal payments to be made one and three years from now. What should the payments be if money now earns 6% compounded quarterly?
    *  \$2756.22  [Click here for full solution](https://youtu.be/IzJnWXet3mA)
<p>&nbsp;</p>


##  5.6  Changing Interest Rates {-}

*  An investment of \$10,000 earns 5% compounded monthly for the first 3 months, 6% compounded quarterly for the next 6 months and 8% compounded monthly for another 3 months.  How much interest was earned over the year?
    *  \$641.59  [Click here for full solution](https://youtu.be/EKpI9sCayx8)
<p>&nbsp;</p>


*  \$15,000 is invested early March and earns 3.75% compounded monthly.  The rate changes to 6% compounded monthly in May and changes to 5.25% compounded monthly in September for the remainder of the calendar year.  How much interest was earned over the lifetime of the investment?
    *  \$669.29  [Click here for full solution](https://youtu.be/RnW9MEwPFqI)
<p>&nbsp;</p>


*  \$5000 is invested January 1 at 3% compounded annually.  The interest rate rises 1% per year.  How much is in the account after 5 years?
    * $6378.51  [Click here for full solution](https://youtu.be/VGcw9sEnDg8)
<p>&nbsp;</p>


##  5.7  Continuously Compounded Interest {-}

*  Jimmy invests \$2,500 in an account earning continuously compounded interest. After 13 years, the account balance reaches \$9,000. What is the interest rate of the account?
    *  9.85% compouned continuously  [Click here for full solution](https://youtu.be/5PenhnhKqSc)
<p>&nbsp;</p>


*  Fred invests a lump sum of money in an account at a rate of 5% that is compounded continuously. After 7 years, the account balance reaches $7500. How much was initially invested?
    *  \$5285.16  [Click here for full solution](https://youtu.be/UrnyLk6kv8Y)
<p>&nbsp;</p>


*  Ken invests a lump sum of money in a bond fund with a fixed annual interest rate of 6% that is compounded continuously. After 15 years, the balance reaches $25,000. How much was initially invested?
    *  \$10,164.24  [Click here for full solution](https://youtu.be/09P4D7jEikM)
<p>&nbsp;</p>


*  You deposit $2500 is deposited in a bank paying an annual interest rate of 3.1%, compounded continuously. Find the balance after 3 years.
    *  \$2743.65  [Click here for full solution](https://youtu.be/MHGBWPbERjg)
<p>&nbsp;</p>


*  If you invest $20,000 at an annual interest rate of 3% compounded continuously, calculate the final amount you will have in the account after 20 years.
    *  \$36,442.38  [Click here for full solution](https://youtu.be/X64AIRSXHz8)
<p>&nbsp;</p>