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 inte
rest compounds daily, what is the interest rate on the account?
2 answers:
Answer:
The interest rate is 42 % on the account .
Step-by-step 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 :
Rate of interest = 0.042 = 42%
So, the interest rate is 42 % on the account .
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 ( <span> <span> <span> 2.4156042989 </span> </span> </span> ) / 7,665
exp = log ( <span> <span> 2.4156042989 </span> </span> ) / 7,665
exp = 0.38302579382 / 7,665
exp = <span> <span> <span> 0.00004997074935681670 </span> </span> </span>
rate = (10^exp -1)* n
rate = (10^<span>0.00004997074935681670 -1) * n
</span>rate = <span><span>(1.0001150685 </span> -1) * 365
</span>rate = <span>(.0001150685) * 365</span>
rate = <span> <span> <span> 0.0420000025 </span> </span> </span>
rate = <span>4.20000025 %
rate = 4.2 %
Yes, it's just that easy. LOL
</span>
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 ( <span> <span> <span> 2.4156042989 </span> </span> </span> ) / 7,665
exp = log ( <span> <span> 2.4156042989 </span> </span> ) / 7,665
exp = 0.38302579382 / 7,665
exp = <span> <span> <span> 0.00004997074935681670 </span> </span> </span>
rate = (10^exp -1)* n
rate = (10^<span>0.00004997074935681670 -1) * n
</span>rate = <span><span>(1.0001150685 </span> -1) * 365
</span>rate = <span>(.0001150685) * 365</span>
rate = <span> <span> <span> 0.0420000025 </span> </span> </span>
rate = <span>4.20000025 %
rate = 4.2 %
Yes, it's just that easy. LOL
</span>
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Step-by-step explanation:
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