If we letbe the initial amount invested andbe the annual interest rate of the CD expressed as a decimal, then at the end ofyears, the amount of moneythat the CD will be worth can be determined by the formula

Substitute,,, and solve for.

The minimum principal to be invested initially is $6,551. However, since we are looking for the multiple of $1,000 that guarantees a minimum final balance of $20,000, we roundupto the nearest such multiple, which is $7,000 - the correct response.

1. Usewhereis the current amount,is the interest rate,is the amount of time in years since the initial deposit, andis the amount initially deposited.

2. Solve for

You currently have $24,596 in your account.

The continuous compound interest formula is

,

whereis the amount of money in the account at the end of the period,is the principal at the beginning,is the annual interest rate in decimal form, andis the number of years over which the interest accumulates. Since Jeff deposits $1,000 per month, we apply this formula twelve times, withequal to the principal at the beginning of each successive month,, and.

We can go ahead and calculate, sinceanddo not change:

这个公式可以写成

At the beginning of January, Jeffrey deposits $10,000. At the end of January, there is

in the account.

At the beginning of February, he again deposits $10,000, so there is now

in the account.

At the end of February, there is

in the account.

Repeat addition of $10,000, then multiplication by 1.006353, ten more times to get the amount of money in the account at the end of December. This will be $125,072.98.

The periodic compound interest formula is

whereis the amount of money in the account at the end of the period,is the principal at the beginning,is the annual interest rate in decimal form,is the number of periods per year at which the interest is compounded, andis the number of years over which the interest accumulates.

Since Sheila deposits $1,000 per month, we apply this formula twelve times, withequal to the principal at the beginning of each successive month,,(monthly interest), and.

We can go ahead and calculate, since,, andremain constant:

.

这个公式可以写成

At the beginning of January, Sheila deposits $10,000. At the end of January, there is

in the account.

At the beginning of February, she again deposits $10,000, so there is now

in the account.

At the end of February, there is

in the account.

Repeat addition of $10,000, then multiplication by 1.006333, ten more times to get the amount of money in the account at the end of December. This will be $125.056.56

Use the formula for compound interest to solve:

"A" is the amount of interest, "P" is the initial amount invested, "r" is the interest rate, "m" is the number of times per year the interest is compounded, and "t" is the number of years the money is invested.

Plug in the appropriate values for the equation:

Because "t" is measure in years, 57 months needs to be converted to years (i.e. 57 months=4.75 years) to solve this equation

Simplify the equation:

Solution: