You deposited 6,000 in a savings account, and after 4 years, your account balance is 7,800. What was the annual interest rate on the account?
Question
You deposited 6,000 in a savings account, and after 4 years, your account balance is 7,800. What was the annual interest rate on the account?
Solution
To solve this problem, we can use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
In this case, we know that:
- A = 7,800
- P = 6,000
- n = 1 (since interest is compounded annually)
- t = 4 years
We want to find r. So, we can rearrange the formula to solve for r:
r = ((A/P)^(1/(nt)) - 1) * n
Substituting the known values:
r = ((7800/6000)^(1/(1*4)) - 1) * 1
r = (1.3^0.25 - 1) * 1
r ≈ 0.067 or 6.7%
So, the annual interest rate on the account was approximately 6.7%.
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