Bob places $5,000 in a special account that accumulates interest compounded annually. Assuming no additional deposits or withdrawals, how much will be in the account after 7 years if the interest rate is 8.5% per annum for first 4 years and 9.25% per annum for the last 3 years?
5000*(1+.085)^4*(1+.0925)^3
To calculate the final amount in the account, we can break down the problem into two parts: the first 4 years and the last 3 years, as the interest rates are different.
Step 1: Calculate the amount after the first 4 years.
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial principal (starting amount)
r = the interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, P = $5,000, r = 8.5% or 0.085 (4 years), n = 1, and t = 4.
A = 5000(1 + 0.085/1)^(1*4)
A = 5000(1 + 0.085)^4
A ≈ $6434.04
After 4 years, the account will have approximately $6434.04.
Step 2: Calculate the amount for the next 3 years.
Using the same formula, but with a different interest rate and years.
Now, P = $6434.04, r = 9.25% or 0.0925 (3 years), n = 1, and t = 3.
A = 6434.04(1 + 0.0925/1)^(1*3)
A ≈ $7918.61
After 3 years, the account will have approximately $7918.61.
Step 3: Calculate the final amount after 7 years.
To find the total amount after both periods, we add the amounts from steps 1 and 2.
Total amount = $6434.04 + $7918.61
Total amount ≈ $14,352.65
Therefore, after 7 years, the account will have approximately $14,352.65.