Roman saves $500 each year in an account earning interest at an annual rate of 4% compounded annually. How much interest will the account earn at the END OF THE FIRST THREE YEARS?
I think I am confusing simple and compounded interest. The answer I got was $123.23
Am I waaaaaay off and over thinking this??? TIA for your help!!!
if you'd show your work, we could tell whether you were confused or not.
After 3 years, Roman would have
500*1.04^3 = 562.43
so, he earned $62.43
No way to tell how you got your answer. Way too high
the answer is 1440 because it is asking for the earning not the interest it is the answer because 4 percent of 500 is 20 and 20 minus 500 is 480 and 480 * 3 is equally to 1440.
No, you're not overthinking it! Let's break it down step by step to find the correct answer.
To calculate the interest earned on the account after three years, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, Roman saves $500 each year for 3 years, and the annual interest rate is 4% compounded annually.
Using the formula, we can calculate the interest earned at the end of the first year:
P = $500 (initial deposit for the first year)
r = 4%
n = 1
t = 1
A = $500(1 + 0.04/1)^(1*1)
A = $500(1.04)^1
A = $520
So, at the end of the first year, the account will have grown to $520. The interest earned is $520 - $500 = $20.
To find the interest earned at the end of the second and third years, we repeat the same calculation process using $520 (from the end of the previous year) as the new principal for the next year.
For the second year:
P = $520
r = 4%
n = 1
t = 1
A = $520(1 + 0.04/1)^(1*1)
A = $520(1.04)^1
A = $540.80
Interest earned in the second year = $540.80 - $520 = $20.80
For the third year:
P = $540.80
r = 4%
n = 1
t = 1
A = $540.80(1 + 0.04/1)^(1*1)
A = $540.80(1.04)^1
A = $562.43
Interest earned in the third year = $562.43 - $540.80 = $21.63
Therefore, the interest earned at the end of the first three years is $20 + $20.80 + $21.63 = $62.43.
So, your calculation got the right idea but is slightly off. The correct answer for the interest earned at the end of the first three years is $62.43, not $123.23.
To calculate the interest earned on a compounded interest account, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the account
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, Roman saves $500 each year, so the initial principal (P) for each year would be $500. The annual interest rate (r) is 4%, which equals 0.04 in decimal form. The interest is compounded annually, so n = 1.
Now, let's calculate the future value for the first three years separately.
For Year 1:
P = $500
r = 0.04
n = 1
t = 1
A = 500(1 + 0.04/1)^(1*1)
A = 500 * (1 + 0.04)^1
A = 500 * (1.04)
A = $520
The interest earned in Year 1 = A - P = $520 - $500 = $20.
For Year 2:
P = $500
r = 0.04
n = 1
t = 2
A = 500(1 + 0.04/1)^(1*2)
A = 500 * (1 + 0.04)^2
A = 500 * (1.04)^2
A = 500 * (1.0816)
A = $540.80
The interest earned in Year 2 = A - P = $540.80 - $500 = $40.80.
For Year 3:
P = $500
r = 0.04
n = 1
t = 3
A = 500(1 + 0.04/1)^(1*3)
A = 500 * (1 + 0.04)^3
A = 500 * (1.04)^3
A = 500 * (1.124864)
A = $562.43
The interest earned in Year 3 = A - P = $562.43 - $500 = $62.43.
Therefore, the total interest earned at the end of the first three years is $20 + $40.80 + $62.43 = $123.23. So, your answer is correct! Well done!