Concept explainers
Future Value In certain savings scenarios, the value
future value, is given by
the amount of the original investment and
at an interest rate of
what is the future value?(continued)
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Your Childs Education You want to begin making regular deposits to finance your childs college education 18 years 216 months in the future. You are able to invest 200 at the end of each month, and you judge that 100, 000 will be needed. That is, you want the future value F of the investment to be 100, 000. Whether you can attain that goal depends on interest rates. If the monthaly interest rate is r as a decimal, then the future value of the investment is given by F=200r1+r216-1 dollars. a. Plot the graph of F along with the target value of 100, 000. Use a horizontal span of 0 to 0.01. b. Fina the monthly rate r that will yield the dsired future value of 100, 000. Round your answer as a percentage to one decimal place. c. What is your total investment in your childs education?arrow_forwardFuture Value Business and finance texts refer to the value of an investment at a future time as its future value. If an investment of P dollars is compounded yearly at an interest rate of r as a decimal, then the value of the investment after t years is given by FutureValue=P1+rt. In this formula, 1+rt is known as the future value interest factor, so the formula above can be written as FutureValue=PFuturevalueinterestfactor Financial officers normally calculate this or look it up in a table a. What future value interest factor will make an investment double? b. Say you have an investment that is compounded yearly at a rate of 9%. Find the future value interest factor for a 7-year investment. c. Use the results from part b to calculate the 7-year future value if your initial investment is 5000.arrow_forwardEquity in a Home When you purchase a home by securing a mortgage, the total paid toward the principal is your equity in the home. Technically, the lending agency calculates your equity by subtracting the amount you still owe on your mortgage from the current value of your home, which may be higher or lower than your principal. Assume that your mortgage is for 350, 000 at a monthly rate of 0.007 as a decimal and that the term of the mortgage is 30 years. Then your equity after k monthly payments is 350, 0001.007k-11.007360-1 dollars. Calculate the equity in your home after 10 years.arrow_forward
- Present Value If you invest P dollars the present value of your investment in a fund that pays an interest rate of r, as a decimal, compounded yearly, then after t years, your investment will have a value of F dollars, which is known as the future value. The discount rare D for such an investment is given by D=1(1+r)t where t is the life, in years, of the investment. The present value of an investment is the product of the future value and the discount rate. Find a formula that gives the present value in terms of the future value, the interest rate, and the life of the investment.arrow_forwardEquity: When you use a mortgage to purchase a home, the leading institution effectively owns the home. You buy back part ownership in the home with each monthly payment. The part you have bought back is your equity in the home. If the mortgage amount is P dollars, the monthly interest rate is r as a decimal, and the term of the mortgage is t months, then your equity after k payments is E(k)=P((1+r)k1)(1+r)t1dollars In this exercise, assume that the mortgage amount is 200,000, the APR is 6so r=0.06/12, and the term of the loan is 30 years 360 months. a. Find a formula for the equity. b. Make a graph of the equity over 360 months, the term of the loan. c. Does the graph show that you have half-ownership in the home halfway through the term of the mortgage?arrow_forwardLending Money For a certain loan, the interest I due at the end of a loan period is given by I=Prt, where P is the principal barrowed, r is the yearly interest rate as a decimal, and t is the number of years since the money was barrowed. What interest is accrued if 3 years ago we barrowed 5000 at an interest rate of 5%?arrow_forward
- Home Equity When you purchase a home by securing a mortgage, the total paid toward the principle is your equity in the home. If your mortgage is for P dollars, and if the term of the mortgage is t months, then your equity E in dollars, after k monthly payments is given by E=P(1+r)k1(1+r)t1 Here r is the monthly interest rate as a decimal, with r=APR/12 Suppose you have a mortgage of 425,000 at an APR of 9% and a term of 30 years. How long does it take for your equity to reach half of the amount of the original mortgage? Round r to four decimal places.arrow_forwardAn Amortization Table Suppose you borrow P dollars at a monthly interest rate of r as a decimal and wish to pay off the loan in t months. Then your monthly payment can be calculated using M=Pr(1+r)t(1+r)t1 dollars. Remember that for monthly compounding, you get the monthly rate by dividing the APR by 12. Suppose you borrow 3500 at a 9 APR meaning that you use r = 0.09/12 in the preceding formula and pay it back in 2 years. a. What is your monthly payment? b. Lets look ahead to the time when the loan is paid off. i. What is the total amount you paid to the bank? ii. How much of that was interest? c. The amount B that you still owe the bank after making k monthly payments can be calculated using the variables r, P, and t. The relationship is given by B=P((1+r)t(1+r)k(1+r)t1) dollars. i. How much do you still owe the bank after 1 year of payments? ii. An amortization table is a table that shows how much you still owe the bank after each payment. Make an amortization table for this loan.arrow_forward
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