Chapter 10.1
$14,800 at 6% compounded semiannually for 4 years. Find the compound amount and the interest.
Compound Amount: $18,748.20
Interest: $3,948.20
Define deflation.
A decrease in the general prices of goods and services
Explain the difference between future value and present value.
Future value is the amount available at a specific date in the future and present value is the amount needed today so that the desired future value will be available when needed.
Define compound interest.
Compound interest is interest calculated on previously credited interest in addition to the original principle.
An investment is put into a bank account that pays 6% interest per year compounded monthly. Given an initial deposit of $4800, (a) use the formula to find the compound amount after 3 years, and (b) find the compound interest.
a) $5,744.07
b) $944.07
A family with an income and spending budget of $36,000 receives an increase in income of 1.5% after taxes in a year when inflation is 2.7%. Find the net gain or loss in purchasing power.
$432 loss in purchasing power
Carlos Mora recently immigrated to the United States from Central America. His family has agreed to help him set aside the cash needed to open a small bakery in 2 years once he completes a program at a culinary institute. Find the amount they must deposit today in an investment account expected to yield 4% compounded quarterly if he needs $95,000 to open the shop in 2 years.
$87,730.60
Name two things that future value depends on.
Amount initially invested, interest rate, compound interest, and length of investment.
Any two of the above.
Sydney Livermore deposits $9,200 with Chase Bank in an investment paying 5% compounded quarterly. Find (a) the compound amount and (b) the interest in 6 years.
a) $12,395.63
b) $3,195.63
Big Brand Tires has $25,000 to deposit in a certificate of deposit for either 2 or 5 years. Assume 3% compounded daily and find the compound amount for both terms.
Compound amount for 2 years = $26,545.85
Compound amount for 5 years = $29,045.68
Samantha Garcia needs $25,000 in 4 years to start her own daycare business. (a) What lump sum should be invested today at 5%, compounded semiannually, to produce the needed amount? (b) How much interest will be earned?
a) $20,518.75
b) $4,481.25
Define inflation.
A increase in the general prices of goods and services.
Becky Hilton has a choice for her investment of $7500. She can invest it in funds she believes she will earn either (a) 8% compounded quarterly for 2 years or (b) 6% compounded semiannually for 5 years. Find the future value of both. (c) Which is larger?
a) $8,787.45
b) $10,079.37
c) the second option (answer b)
Beatrice and Jake Bellisme are retired and they have $225,500 in a savings account at Chase Bank paying 3.0% compounded daily. What is their gain or loss in purchasing power from interest in a year in which inflation is 3.5%?
$1,052.71 loss in purchasing power
Village Hardware expands its business at a cost of $20,000. They expect that the investment will grow at a rate of 10% per year compounded annually for the next 4 years. (a) Find the future value of the investment. (b) Find the present value of the amount found in part (a) at a rate of 6% compounded annually. Round to the nearest dollar at each step.
a) $29,282
b) $23,193.98
Name one effect of deflation.
People became worried about their savings and jobs
Thus people postponed purchases, demand fell, and sales at firms plummeted.
Managers responded by laying off even more workers, causing higher unemployment and even more fear.
Managers at Bank of America are debating about whether to lend $900,000 to a contractor at 7% simple interest or to a factory at 6% compounded monthly. Either loan would be for 9 months. Identify the loan that would pay more interest and how much additional interest it would pay. Then find the effective interest rate for the simple interest loan and the compound interest loan to the nearest tenth of a percent.
Simple interest loan would make you pay more ($5,930.48 more).
Effective interest rate for simple interest = 5.3%
Effective interest rate for compound amount = 4.6%
On April 1, MVP Sports opened a savings account at Bank of America with a deposit of $17,500. A withdrawal of $5000 was made 21 days later, another withdrawal of $980 was made 12 days before July 1. Assume 3.5% compounded daily. Find (a) the balance on July 1 and (b) the interest earned through that date.
a) $11,637.28
b) $117.28
John Fernandez figures his bike shop is worth $88,000 if sold today and that it will grow in value at 8% per year compounded annually for the next 6 years. If he sells the business, the funds will be invested at 5% compounded semiannually. (a) Find the future value of the shop. (b) What price should he insist on at this time if he sells the business?
a) $139,644.94
b) $103,850
Name one effect of inflation.
Inflation can reduce the ability of a family to buy products and services.
Inflation can erode purchasing power even though pay raises are received every year.
Retired people are particularly concerned with inflation, since they live off of Social Security payments and their estate. (some people may have to go back to work).