Question

Suppose that $6500 is placed in an account that pays 6% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding. (a) Find the amount in the account at the end of 1 year. (b) Find the amount in the account at the end of 2 years.

Answer 1

To calculate the amount in the account at the end of each year, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

Where:
A = Amount in the account at the end of the specified time period
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Number of years

In this case:
P = $6500
r = 0.06 (6% expressed as a decimal)
n = 1 (compounded once per year)

(a) To find the amount in the account at the end of 1 year, we substitute the given values into the formula:

A = 6500(1 + 0.06/1)^(1*1)
A = 6500(1 + 0.06)^1
A = 6500(1.06)
A = $6890

The amount in the account at the end of 1 year is $6890.

(b) To find the amount in the account at the end of 2 years, we substitute the values into the formula again:

A = 6500(1 + 0.06/1)^(1*2)
A = 6500(1 + 0.06)^2
A = 6500(1.06)^2
A = 6500(1.1236)
A = $7292.40

The amount in the account at the end of 2 years is $7292.40.