The Bank of Utopia offers an interest rate of 100% per annum with various options as to how the interest may be added. Gopal invests $1000 and considers the following options. Option A Interest added annually at the end of the year. Option B Interest of 50% credited at the end of each half-year. Option C, D, E, . . . The Bank is willing to add interest as often as required, subject to (interest rate) x (number of credits per year) = 100. Investigate to find the maximum possible amount in Gopal's account after one year.

Work the problem.

Kinisha borrowed $2000 from a credit union at 12 percent annual interest and borrowed$500 from her aunt at 7 percent annual interest. What single rate of interest on $2500 results in the same total amount of interest?

The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date. Find the present value of $100,000 if interest is paid at a rate of 8% per year, compounded monthly, for 5 years.

P dollars invested at interest rate r compounded annually increases to an amount $A=P(1+r)^{2}$ in 2 years. An investment of $5000 is to increase to an amount greater than$5500 in 2 years. The interest rate must be greater than what percent?

In order to find the future worth, F, from a present amount, P, 5 years from now at an interest rate of 12% per year, compounded quarterly, what interest rate must be used in the F/P factor, (F/P,i%,n), when n is (a) 5, (b) 10, and (c) 20?

Austin deposits $2,250 into a one-year CD at an interest rate of 5.3%, compounded daily. How much interest did the account earn during the year?

Solve each problem involving compound interest. See the examples in this section.

Find the required annual interest rate to the nearest tenth of a percent for $\$ 5000$ to grow to $\$ 8400$ if interest is compounded quarterly for $8 \mathrm{~yr}$.

Money deposited in a certain bank doubles every 13 years. The bank compounds interest continuously. What annual interest rate does the bank offer?

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Joe borrowed $2,000 from the bank at a rate of 7% simple interest per year. How much interest did he pay in 5 years?

Express the annual interest rate as a percentage, rounded to the nearest integer. In Alabama, finance charges on a payday loan may not exceed 17.5% of the amount advance d. Find the annual interest rate if $500 is borrowed for 10 days at the maximum allowable charge.

A taxpayer who pays 22% in taxes each year has these two accounts. Account 1: $10,000 is placed in a tax-deferred account that pays 2.1% interest compounded annually for 25 years. Account 2:$10,000 is placed in a taxable account that pays 2.1% interest compounded annually for 25 years. Since the taxpayer pays 22% of all income in taxes, 22% of the interest he makes each year will go toward taxes. Therefore, his annual interest rate in actuality is 22% less than the 2.1% quoted rate. What is his real annual interest rate?

Kristin deposited $9,000 in an account that has an annual interest rate of 2.1% compounded monthly. How much interest will she earn at the end of one month?

A person invests $8,500 in a bank that compounds interest continuously. If the investment doubles in 10 years, what is the (annual) rate of interest (correct to the nearest tenth percent)?