Question

Use the formula P(1 + r)t to solve the problems. The amount that results when $2,000 is compounded at 8% annually over six years is $ ___.

a) $3,564.48
b) $3,456.00
c) $3,456.78
d) $2,986.88

The interest earned in this case is $___.

a) $1,564.48
b) $1,456.00
c) $1,456.78
d) $986.88

Answer 1

To find the amount after compounding and interest earned, substitute the values into the compound interest formula. The amount that results when $2,000 is compounded at 8% annually over six years is $3,187.70. The interest earned in this case is $1,187.70.

Step-by-step explanation:

To solve this problem, we need to use the formula for compound interest, which is P(1 + r)^t. In this case, the principal amount (P) is $2,000, the interest rate (r) is 8% (or 0.08 as a decimal), and the time period (t) is 6 years.

Let's substitute these values into the formula:

$2,000(1 + 0.08)^6

Simplifying the exponent:

$2,000(1.08)^6

Now, we can calculate the answer:

$2,000(1.593848)

= $3,187.70

Therefore, the amount that results when $2,000 is compounded at 8% annually over six years is $3,187.70.

To find the interest earned, we can subtract the principal amount from the total amount:

$3,187.70 - $2,000 = $1,187.70

So, the interest earned in this case is $1,187.70.