Question

To start a new business Beth deposits $2000 at the end of each six-month period in an account that pays 7%, compounded semiannually. How much will she have at the end of 8 years?

Answer 1

The end of 8 years, Beth will have approximately $3498 in the account if she deposits $2000 at the end of each six-month period at an interest rate of 7%, compounded semiannually.

To calculate the future value of Beth's deposits, you can use the formula for compound interest:

`A=P* (1+ (r)/(n) )^{nt`

Where:

A is the future value of the investment/deposit.

P is the principal amount deposited at the end of each period, which is $2000 in this case.

r is the annual interest rate, which is 7% or 0.07 in decimal form.

n is the number of times the interest is compounded per year, which is semiannually (twice a year).

t is the number of years.

Given that Beth deposits $2000 at the end of each six-month period (semiannually) for 8 years at an interest rate of 7% compounded semiannually, let's calculate the future value:

First, calculate the number of compounding periods:

n=2×number of years=2×8=16 compounding periods

Now, substitute these values into the formula:

`A=2000* (1+ 0.07/2 )^(2*8)`

`A=2000* (1+0.035)^(16)`

`A=2000* (1.035)^{16`

Let's calculate A:

`A=2000*1.035^16 = 2000* 1.749= 3498`

Therefore, at the end of 8 years, Beth will have approximately $3498 in the account if she deposits $2000 at the end of each six-month period at an interest rate of 7%, compounded semiannually.

Answer 2

Okay, here we have this: