Question

Kate currently has an account balance of $7,194.66. She opened the account 21 years ago with a deposit of $2,978.41. If the interest compounds daily, what is the interest rate on the account?

Answer 1

Use the attached formula.
exp = [log (total / principal) / n*years]
where "n" is compounding periods per year
exp = [log (7,194.66 / 2,978.41) / (365*21)
exp = log ( 2.4156042989 ) / 7,665
exp = log ( 2.4156042989 ) / 7,665
exp = 0.38302579382 / 7,665
exp = 0.00004997074935681670

rate = (10^exp -1)* n
rate = (10^0.00004997074935681670 -1) * n
rate = (1.0001150685 -1) * 365
rate = (.0001150685) * 365
rate = 0.0420000025
rate = 4.20000025 %
rate = 4.2 %

Yes, it's just that easy. LOL

Answer 2

The interest rate is 42 % on the account .

Explanation:

Kate currently has an account balance of $7,194.66.

She opened the account 21 years ago with a deposit of $2,978.41.

So, Amount = $7,194.66.

Principal = $2,978.41.

Time = 21 years

No. of compounds = 365 since we are given that compounded daily.

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

`7194.66=2978.41(1+(r)/(365))^(365 * 21)`

`r=0.042`

Rate of interest = 0.042 = 42%

So, the interest rate is 42 % on the account .