you put $500 in an account that earns 4% annual interest. the interest earned each year is added to the…

you put $500 in an account that earns 4% annual interest. the interest earned each year is added to the principal to create a new principal. find the total amount in your account after each year for 3 years.\n\nyear 1 = $ 520 \n\nyear 2 = $ 540.8 \n\nyear 3 = $\\square

you put $500 in an account that earns 4% annual interest. the interest earned each year is added to the principal to create a new principal. find the total amount in your account after each year for 3 years.\n\nyear 1 = $ 520 \n\nyear 2 = $ 540.8 \n\nyear 3 = $\\square

Answer

Explanation:

Step1: Identify the formula for compound interest

The formula for compound interest when interest is compounded annually is ( A = P(1 + r)^t ), but since we are calculating year by year, for each year, the amount ( A ) at the end of the year is the principal ( P ) at the start of the year multiplied by ( (1 + r) ), where ( r ) is the annual interest rate (in decimal). Here, ( r = 4%= 0.04 ), and for year 3, the principal at the start of year 3 is the amount at the end of year 2, which is ( $540.8 ).

Step2: Calculate the amount for year 3

We use the formula ( A = P(1 + r) ), where ( P = 540.8 ) and ( r = 0.04 ). So, ( A=540.8\times(1 + 0.04) ) ( A = 540.8\times1.04 ) First, calculate ( 540.8\times1 = 540.8 ) and ( 540.8\times0.04=21.632 ) Then, add them together: ( 540.8+21.632 = 562.432 )

Answer:

( 562.432 ) (or in dollar format, $562.432, usually rounded to two decimal places as $562.43 or $562.43 depending on the context, but the exact value from the calculation is 562.432)