Julia invests $80,000 in an account which pays 5.97% interest compounded quarterly. After 20 years and 6 months, how much money will she have in the account?
Use: A = P(1-R)^n
80000(1-5.97%/4)^82
we get n (82) from:
4*20years + 4*6months = 24months/2years
quarterly = 4 parts (of a year)
Type that into a calculator and you should get your answer.
Still don't understand how you got 82.
To calculate the amount of money Julia will have in the account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = the number of years
In this case, Julia's initial investment is $80,000, the annual interest rate is 5.97% (or 0.0597 in decimal form), and interest is compounded quarterly. The time is given as 20 years and 6 months, which is 20.5 years.
Let's plug these values into the formula:
A = 80000(1 + 0.0597/4)^(4 * 20.5)
Now let's solve it step by step:
Step 1: Divide the annual interest rate by the number of compounding periods per year:
0.0597 / 4 = 0.014925 (rounded to 6 decimal places)
Step 2: Multiply the number of compounding periods per year by the total number of years:
4 * 20.5 = 82
Step 3: Add 1 to the result of step 1:
1 + 0.014925 = 1.014925 (rounded to 6 decimal places)
Step 4: Raise the result of step 3 to the power of the result of step 2:
1.014925^82 = 3.1880574717 (rounded to 10 decimal places)
Step 5: Multiply the final result by the principal amount:
80000 * 3.1880574717 = $255,044.60 (rounded to 2 decimal places)
Therefore, after 20 years and 6 months, Julia will have approximately $255,044.60 in the account.