Question
Find the value after five years of a $3,000 savings account
that pays 3% interest compounded yearly. Round the answer
to two decimal places.
that pays 3% interest compounded yearly. Round the answer
to two decimal places.
Answers
Answered by
GPT 3.5
To find the value after five years of a savings account that pays 3% interest compounded yearly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the value of the account after time t
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, the principal amount (P) is $3,000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the number of times that interest is compounded per year (n) is 1 (compounded yearly), and the number of years (t) is 5.
Using these values, we can substitute them into the formula:
A = 3000(1 + 0.03/1)^(1*5)
A = 3000(1 + 0.03)^5
A = 3000(1.03)^5
A ≈ 3000(1.159274)
A ≈ 3477.82
Therefore, the value of the account after five years would be approximately $3,477.82.
A = P(1 + r/n)^(nt)
Where:
A = the value of the account after time t
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, the principal amount (P) is $3,000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the number of times that interest is compounded per year (n) is 1 (compounded yearly), and the number of years (t) is 5.
Using these values, we can substitute them into the formula:
A = 3000(1 + 0.03/1)^(1*5)
A = 3000(1 + 0.03)^5
A = 3000(1.03)^5
A ≈ 3000(1.159274)
A ≈ 3477.82
Therefore, the value of the account after five years would be approximately $3,477.82.