Hi, can someone please walk me through this? I forgot how to do this and I lost my notes about it from last year
Audrey deposited $2,800 in a savings account that pays 2.65% interest compounded annually. What is the total value of the account after 7 years?
Sure! I can help you with that.
To find the total value of the savings account after 7 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total value of the account after the specified time period
P = the initial principal (the amount initially deposited)
r = the interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, Audrey deposited $2,800 (P), the interest rate is 2.65% (or 0.0265 in decimal form) compounded annually, so n = 1, and the time period is 7 years (t).
Plugging the values into the formula, we get:
A = 2800(1 + 0.0265/1)^(1*7)
Now let's solve the equation step by step.
1. First, we need to simplify the expression inside the parentheses:
1 + 0.0265/1 = 1 + 0.0265 = 1.0265
2. Now, we raise the simplified value to the power of the number of years:
(1.0265)^(1*7) = 1.0265^7 ≈ 1.1935
3. Finally, we substitute the calculated value back into the formula:
A = 2800(1.1935)
Now, multiply these two values to get the total value of the account after 7 years.
A ≈ 2800 * 1.1935 ≈ $3,341.80
So, the total value of Audrey's savings account after 7 years will be approximately $3,341.80.
for annual compounding
total value = initial (1 + interest)^years
t.v. = 2800 (1 + .0265)^7