Question

if i deposit $5000 in an account that compounds interest monthly and 3.5 years later the account totals$6165, what annual rate of interest did the account pay?

Answer 1

The annual interest rate for a $5000 deposit that compounded to $6165 after 3.5 years with monthly compounding interest is approximately 6.48%.

Step-by-step explanation:

To find the annual rate of interest the account paid, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

In your case:

• A = $6165
• P = $5000
• n = 12 (since the interest is compounded monthly)
• t = 3.5 years

We need to find the annual interest rate, r. Rearranging the formula to solve for r, we get:

r = n[(A/P)^(1/nt) - 1]

Plugging the values into the formula, we get:

r = 12[(6165/5000)^(1/(12*3.5)) - 1]

Calculating the values inside the brackets first:

(6165/5000)^(1/(12*3.5)) = (1.233)^(1/42)

≈ 1.0054

Now, we subtract 1 and then multiply by n:

r ≈ 12 * (1.0054 - 1)

= 12 * 0.0054

r ≈ 0.0648 or 6.48%

The annual interest rate the account paid was approximately 6.48%.