Find the value after five years of a $3000 savings account that pays 3% interest compounded daily
To find the value of the savings account after five years with daily compounding interest, we will use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the ending balance
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
P = $3000
r = 3% = 0.03
n = 365 (daily compounding)
t = 5
Plugging in these values into the formula, we have:
A = 3000(1 + 0.03/365)^(365*5)
Calculating the exponent:
(1 + 0.03/365)^(365*5) ≈ 1.03013748852
Multiplying the principal amount by the exponent:
A ≈ 3000 * 1.03013748852 ≈ $3195.41
Therefore, the value of the savings account after five years with daily compounding interest is approximately $3195.41.