Roiger made deposits of $900 semiannually to the bank, which pays 6% interest compounded semiannually. After 7 yrs., he makes no more deposits. What would be the balance in the account 8 yrs. later from the last deposit?

Didn't you ask the same question on Tuesday ?

http://www.jiskha.com/display.cgi?id=1312312482

"Yes but the answer didn't make sense and in fact, was not what my professor was looking for.

You are right, after I read it more carefully, one tiny change has to be made

Instead of

Amount at the last deposit
= 900[ 1.03^14 - 1]/.03 = 15377.69

Value at the end of 8 years = 15377.69(1.03)^2 = 16314.19
change it to:

Amount at the last deposit
= 900[ 1.03^14 - 1]/.03 = 15377.69

Value 8 years after last deposit = 15377.69(1.03)^16 = 24676.68


Notice I changed the exponent of 2 in the last line to 16
I had it as 8 years from now, instead of 8 years after the last deposit.

Thank you I believe that's what I got and now it makes sense. Thanks

To find the balance in the account 8 years later from the last deposit, we need to calculate the future value of the deposits.

First, let's calculate the number of deposit periods. Since Roiger makes deposits semiannually and the duration is 7 years, there would be 14 deposit periods (2 deposits per year x 7 years).

Now, let's calculate the future value of the deposits after 7 years. We can use the formula for future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where:
FV = Future Value
P = Periodic payment (deposit amount)
r = Interest rate per deposit period
n = Number of deposit periods

In this case:
P = $900
r = 6% compounded semiannually, so the interest rate per deposit period is 3%
n = 14

Substituting the values into the formula:

FV = $900 * [(1 + 0.03)^14 - 1] / 0.03

Calculating this, we find that the future value of the deposits after 7 years is approximately $13,785.48.

Now, to find the balance in the account 8 years later from the last deposit, we need to calculate the future value of this amount. Since there is no additional deposit in the 8th year, we only need to consider the interest earned on the previous balance.

Using the formula for compound interest:

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

Where:
A = Future Value
P = Principal amount (previous balance)
r = Interest rate per deposit period
n = Number of deposit periods per year
t = Time in years

In this case:
P = $13,785.48
r = 6% compounded semiannually, so the interest rate per deposit period is 3%
n = 2 (semiannual deposits)
t = 1 (8 years from the last deposit divided by the deposit period of 2)

Substituting the values into the formula:

A = $13,785.48 * (1 + 0.03/2)^(2*1)

Calculating this, we find that the balance in the account 8 years later from the last deposit would be approximately $14,662.92.