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# Future Value

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You need to accumulate \$10,000. To do so you plan to make deposits of \$1250 per year, with the first payment being made a year from today in a bank account that pays 12 percent interest. Your last deposit will be less than \$1250 if less is need to round out to \$10,000. How many years will it take you to reach your \$10,000 goal, and what will be the last deposit?

#### Solution Preview

You need to accumulate \$10,000.  To do so you plan to make deposits of \$1250 per year, with the first payment being made a year from today in a bank account that pays 12 percent interest.  Your last deposit will be less than \$1250 if less is ...

#### Solution Summary

The solution calculates the number of years required to achieve a future value, given the value of annual deposits (annuity).

\$2.19

## interest rate, compound amount and loans

Section 5.1
#2 Find the interest on each of these loans
\$35,000 at 6% for 9 months

#4 Find the interest on each of these loans
\$1875 at 5.3% for 7 months

#8 Find the interest on each of these loans
\$8940 at 9%; loan made on May 7 and due September 19

#16 Find the future value of each of these loans
\$3475 loan at 7.5% for 6 months

#18 Find the future value of each of these loans
\$24,500 loan at 9.6% for 10 months

#22 Find the present value of each future amount
\$48,000 for 8 months; money earns 5%

#26 The given Treasury bills were sold in August 2008 find:
a) The price of the T bill and
b) The actual interest rate paid by the Treasury
Six month \$18,000 T-bill with discount rate 1.925%

#30 An accountant for a corporation forgot to pay the firm's income tax of \$725,896.15 on time. The government charged a penalty of 9.8% interest for the 34 days the money was late. Find the total amount (tax and penalty) that was paid

#36 What is the time period of a \$10,000 loan at 6.75% in which the total amount of interest paid was \$618.75?

#44 WORK THE NEXT PROBLEM IN WHICH YOU ARE TO FIND THE ANNUAL SIMPLE INTEREST RATE. CONSIDER ANY FEES, DIVIDENDS OR PROFITS AS PART OF THE TOTAL INTEREST
Jerry Ryan borrowed \$8000 for nine months at an interest rate of 7%. The bank also charges a \$100 processing fee. What is the actual interest rate for this loan?

Section 5.2
#8 Find the compound amount of the following deposit
\$1000 at 6% compounded annually for 10 years

#10 Find the compound amount of the following deposit
\$15,000 at 4.6% compounded semiannually for 11 years

#14 Find the amount of interest earned by the following deposits
\$22,000 at 5% compounded annually for 8 years

#18 Find the amount of interest earned by the following deposits
\$27,630.35 at 4.6% compounded quarterly for 3.9 years

#22 Find the interest rate with annual compounding that makes the statement true
\$9000 grows to \$17,118 in 16 years

#24 Find the face value to the nearest dollar of the zero-coupon bond
10 year bond at 4.1%; price \$13,328

#26 Find the face value to the nearest dollar of the zero-coupon bond
25 year bond at 4.4%; price \$10,106

#32 Find the APY corresponding to the given nominal rates
4.7% compounded semiannually

#36 Find the present value of the given future amounts
\$8500 at 6% compounded annually for 9 years

#44 If money can be invested at 6% compounded annually, which is larger, \$10,000 now or \$15,000 in 6 years? Use present value to decide

#46 A developer needs \$80,000 to buy land. He is able to borrow the money at 10% per year compounded quarterly. How much will the interest amount to if he pays off the loan in 5 years?

#52 Two partners agree to invest equal amounts in their business. One will contribute \$10,000 immediately. The other plans to contribute an equivalent amount in 3 years, when she expects to acquire a large sum of money. How much should she contribute at that time to match her partner's investment now, assuming an interest rate of 6% compounded semiannually?

#66 USE THE APPROACH BELOW TO FIND THE TIME IT WOULD TAKE FOR THE GENERAL LEVEL OF PRICES IN THE ECONOMY TO DOUBLE AT THE AVERAGE ANNUAL INFLATION RATES
THE QUESTION IS 4%
Suppose that the inflation rate is 3.5% (which means that the overall level of prices is rising 3.5% a year). How many years will it take for the overall level of prices to double?
We want to find the number of years it will take for \$1 worth of goods or services to cost \$2. Think of \$1 as the present value and \$2 as the future value, with an interest rate of 3.5% compounded annually.

Section 5.3
#4 Find the future value of the ordinary annuities with the given payments and interest rates
R = \$20,000, 4.5% interest compounded annually for 12 years

#8 Find the future value of the ordinary annuities with the given payments and interest rates
R = \$20,000, 6% interest compounded quarterly for 12 years

#10 Find the final amount rounded to the nearest dollar in the following retirement accounts, in which the rate of return on the account and the regular contribution change over time.
\$500 per month invested at 5%, compounded monthly, for 20 years; then \$1000 per month invested at 8%, compounded monthly for 20 years.

#14 Find the amount of each payment to be made into a sinking fund to accumulate the given amounts. Payments are made at the end of each period
\$65,000; money earns 6% compounded semiannually for 4 ½ years

#20 Find the interest rate needed for the sinking fund to reach the required amount. Assume that the compounding period is the same as the payment period
\$100,000 to be accumulated in 15 years; quarterly payments of \$1200

#26 Find the future value of annuity due
Payments of \$1050 for 8 years at 3.5% compounded annually

#28 Find the future value of each annuity due
Payments of \$25,000 for 12 years at 6% compounded annually

#34 Find the payment that should be used for the annuity due whose future value is given. Assume that the compounding period is the same as the payment period.
\$12,000 annual payments for 6 years; interest rate 5.1%

#42 Hassi is paid on the first day of the month, and \$80 is automatically deducted from his pay and deposited in a savings account. If the account pays 7.5% interest compounded monthly, how much will be in the account after 3 years and 9 months?

#44 Jasspreet Kaur deposits \$2435 at the beginning of each semiannual period for 8 years in an account paying 6% compounded semiannually. She then leaves that money alone, with no further deposits, for an additional 5 years. Find the final amount on deposit after the entire 13 year period.

Section 5.4
#2 Find the present value of each ordinary annuity
Payments of \$890 each year for 16 years at 6% compounded annually

#8 Find the amount necessary to fund the given withdrawals
Yearly withdrawals of \$1200 for 14 years; interest rate is 5.6% compounded annually

#12 Find the payment made by the ordinary annuity with the given present values
\$45,000 monthly payments for 11 years; interest rate is 5.3% compounded monthly

#16 Find the lump sum deposited today that will yield the same total amount as payments of \$10,000 at the end of each year for 15 years at each of the given interest rates
4% compounded annually

#20 Find the price a purchaser should be willing to pay for the given bond. Assume that the coupon interest is paid twice a year.
\$20,000 bond with coupon rate 4.5% that matures in 8 years; current interest rate is 5.9%

#28 Find the payment necessary to amortize each of the given loans
\$140,000; 12% compounded quarterly; 15 quarterly payments

#34 Find the monthly house payment necessary to amortize the given loan
\$96,511 at 8.57% for 25 years

#40 USE THE FOLLOWING TABLE TO SOLVE THIS PROBLEM
PAYMENT AMT OF PAYMENT INTEREST FOR PERIOD PORTION TO PRINCIPAL PRINCIPAL END PERIOD
0 ---- --------- ---------- \$1000.00
1 \$88.85 \$10.00 \$78.85 921.15
2 88.85 9.21 79.64 841.51
3 88.85 8.42 80.43 761.08
4 88.85 7.61 81.24 679.84
5 88.85 6.80 82.05 597.79
6 88.85 5.98 82.87 514.92
7 88.85 5.15 83.70 431.22
8 88.85 4.31 84.54 346.68
9 88.85 3.47 85.38 261.30
10 88.85 2.61 86.24 175.06
11 88.85 1.75 87.10 87.96
12 88.84 .88 87.96 0
Using the above table how much of the 10th payment is used to reduce the debt?
#44 Find the cash value of the lottery jackpot to the nearest dollar. Yearly jackpot payments begin immediately (26 for mega millions and 30 for powerball). Assume the lottery can invest at the given interest rate.
Powerball; \$207 million; 5.78% interest

#50 A student education loan has two repayment options. The standard plan repays the loan in 10 years with equal monthly payments. The extended plan allows from 12 to 30 years to repay the loan. A student borrows \$35,000 at 7.43% compounded monthly.
Find the monthly payment and total interest paid under the standard plan

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