10 years ago raj deposited $5000 into an investment account with intrest compound quarterly. for the first 5 years the intrest rate was 6%
and for the next 5 years the interest rate changed to 4.5% how much money is in the account now
I will assume that the second rate was also compounded quarterly
quarterly rate for first 5 years = .06/4 = .015
quarterly rate for last 5 years = .045/4 = .01125
amount after first 5 years = 5000(1.015)^20
and after the last 5 years
= 5000(1.015)^20 (1.01125)^20
= $8422.90
To calculate the amount of money in the account now, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money in the account
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
For the first 5 years, the interest rate was 6%. Since the interest is compounded quarterly, n = 4. The annual interest rate in decimal form is 6% / 100 = 0.06. The principal amount is $5000.
Using these values, we can calculate the amount of money accumulated after the first 5 years:
A1 = 5000(1 + 0.06/4)^(4*5)
Next, for the next 5 years, the interest rate changed to 4.5%. Again, we have quarterly compounding, so n = 4. The annual interest rate in decimal form is 4.5% / 100 = 0.045. The principal amount is the accumulated value after the first 5 years, A1.
Using these values, we can calculate the amount of money accumulated after the next 5 years:
A2 = A1(1 + 0.045/4)^(4*5)
Finally, to find the total amount of money in the account now, we add A1 and A2:
Total Amount = A1 + A2
By substituting the values into the formulas, you can calculate the final amount of money in the account now.