An accountant deposits 100 per month into an account that pays 8% per year compounded quarterly ( no interperiod compounding) How much will she have in 10 years

To calculate the value of the account after 10 years, you need to consider the regular monthly deposits and the interest earned on the account.

First, let's calculate the total number of periods over 10 years, given that interest is compounded quarterly.

Quarterly interest compounding means there are 4 compounding periods in a year. So, over 10 years, there will be a total of 10 * 4 = 40 compounding periods.

Now, let's calculate the value of the monthly deposits over 10 years.

Since the accountant deposits $100 per month, the total amount contributed over 10 years can be calculated as:
Total Contribution = Monthly Deposit * Total Number of Months
Total Contribution = 100 * 12 * 10 = $12,000

Next, let's calculate the interest earned on the account over 10 years.

To calculate the compound interest, we can use the formula:
Future Value = Principal Amount * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)

Here, the principal amount is the total contributions, and the interest rate is 8% (or 0.08) per year.

Future Value = $12,000 * (1 + (0.08 / 4))^(40)
Future Value = $12,000 * (1 + 0.02)^(40)
Future Value = $12,000 * (1.02)^(40)
Future Value ≈ $24,279.16 (rounded to the nearest cent)

Therefore, the accountant will have approximately $24,279.16 in the account after 10 years.

To calculate how much the accountant will have in 10 years, we need to use the formula for compound interest:

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

Where:
A = the amount of money at the end of the time period
P = the principal amount (initial deposit)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years

In this case, the principal amount (P) is $100, the annual interest rate (r) is 8% or 0.08, and the number of times interest is compounded per year (n) is 4 (quarterly).

Let's plug these values into the formula:

A = 100(1 + 0.08/4)^(4*10)
A = 100(1 + 0.02)^40
A = 100(1.02)^40
A ≈ 100(1.818397)

Calculating this, we find:

A ≈ $181.84

Therefore, the accountant will have approximately $181.84 in the account after 10 years.