Question

Your birthday is next week and instead of other presents, your parents promised to give you $1,900 in cash. Since you have a part-time job and, thus, don’t need the cash immediately, you decide to invest the money in a bank CD that pays 7.40 percent, compounded quarterly, for the next two years. How much money can you expect to earn in this period of time? (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answer to the nearest penny.) Value of investment after 2 years $________

Answer 1

The value of a $1,900 CD with a 7.40% interest rate, compounded quarterly after 2 years is approximately $2205.19 when rounded to the nearest penny.

Step-by-step explanation:

To calculate the future value of your investment, which is a certificate of deposit (CD) with a specific interest rate that is compounded a certain number of times per year, you can use the following compound interest formula:

A = P(1 + r/n)^(nt),

where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal form).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

In your case:

• P = $1,900
• r = 7.40% or 0.074 (as a decimal)
• n = 4 (compounded quarterly)
• t = 2 years

So the equation to find out how much money you can expect to earn in two years would be:

A = 1900(1 + 0.074/4)^(4*2)

First, calculate the inside of the parentheses and the exponent:

1 + 0.074/4 = 1.0185 (rounded to four decimal places)

Then raise this to the power of 8, which is 4 quarters per year times 2 years:

(1.0185)^8 ≈ 1.160416 (rounded to six decimal places)

Now multiply this by the initial investment:

1900 * 1.160416 ≈ $2205.19

This means at the end of 2 years, your investment would grow to $2205.19 when rounded to the nearest penny.