Question

suppose 7,500 is invested at 1.5%, compounded continuously. what will the account balance be in 16 years?​

Answer 1

`\boxed {\boxed {\sf \$9,534.37}}`

Explanation:

The formula for continuously compounded is:

`A=Pe^(rt)`

where P is the principal amount, r is the interest rate as a decimal, and t is the amount of time.

The principal amount is $7,500 and time is 16 years. The interest rate is 1.5%. Convert this to a decimal- divide by 100 or move the decimal places two spots to the left.

• 1.5/100= 0.015 or 1.5 --> 0.15 --> 0.015

Now we know all the values and can substitute them into the formula.

`P= 7500 \\r= 0.015 \\t= 16`

`A= 7500(e^(0.015*16))`

Solve the multiplication in the exponent first.

`A= 7500(e^(24))`

Solve the exponent.

`A= 7500 (1.27124915)`

`A=9534.368627`

Round to the nearest cent (hundredth place). The 8 in the thousandth place tells us to the round the 6 to a 7.

`A=9534.37`

The account balance will be $9,534.37 after 16 years.