An initial investment of $480 is invested for 4 years in an account that earns 16% interest, compounded quarterly. What is the amount of money in the account at the end of the period?
At 16% interest compounded quarterly, the value of the account increases by a factor 1.04 every three months. That is becasue 1/4 of 16% is (4%) added to it. Four years is 16 quarters. The value of the account is then
$480.00*(1.04)^16 = $899.03
invest 23,000 in a saving account 4.25 interest compouned quartley
59943.75
To calculate the amount of money in the account at the end of the period, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the initial investment amount
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the initial investment (P) is $480, the annual interest rate (r) is 16%, interest is compounded quarterly (n = 4 times per year), and the investment period (t) is 4 years. Let's plug in these values into the formula and solve for A:
A = 480(1 + 0.16/4)^(4*4)
A = 480(1 + 0.04)^16
A = 480(1.04)^16
To solve this equation, we will break it down into steps:
Step 1: Calculate (1.04)^16 using a calculator.
(1.04)^16 ≈ 1.74585 (rounded to 5 decimal places)
Step 2: Multiply the result from Step 1 by the initial investment (480).
A ≈ 480 * 1.74585
A ≈ 837.804
Therefore, the amount of money in the account at the end of the 4-year period is approximately $837.80.