Suppose that $20000 is invested at 7% interest compounded annually. Find that amount of money in the account after 1 year?
need it broken down in algebra
check your compound interest formula:
A = P(1+r/n)^(nt)
A = 20000 (1 + 0.07/1)^(1*1) = 1400
To find the amount of money in the account after 1 year, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the final amount of money in the account
P is the principal amount (initial investment)
r is the annual interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $20000, the annual interest rate (r) is 7% or 0.07, the interest is compounded annually (n = 1), and the number of years (t) is 1.
Plugging these values into the formula, we get:
A = 20000(1 + 0.07/1)^(1*1)
Simplifying further:
A = 20000(1 + 0.07)^1
Using the order of operations (PEMDAS), we first calculate 1 + 0.07:
A = 20000(1.07)^1
Finally, we can evaluate (1.07)^1 and multiply it by 20000:
A = 20000(1.07) ≈ $21400
Therefore, the amount of money in the account after 1 year would be approximately $21,400.
To find the amount of money in the account after 1 year with an initial investment of $20,000 and an interest rate of 7% compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount in the account
P is the principal amount (initial investment)
r is the annual interest rate (expressed as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $20,000, the annual interest rate (r) is 7% (or 0.07 as a decimal), the number of compounding periods per year (n) is 1 (since it is compounded annually), and the number of years (t) is 1.
Plugging these values into the formula gives us:
A = 20000(1 + 0.07/1)^(1*1)
= 20000(1 + 0.07)^1
= 20000(1.07)^1
= 20000 * 1.07
= 21400
Therefore, the amount of money in the account after 1 year would be $21,400.