Answer: 39 years, 10 months
Step-by-step explanation:
Here is the complete question:
Odessa deposited $1,347.80 into a savings account with an interest rate of 3.3% compounded monthly. About how long will it take for the account to be worth $5,000?
The formula for compound interest is:
= A=P(1+i)^n,
where
P =initial investment = $1347.80
i = interest rate = 3.3% = 0.033/12 = 0.00275
n = number of periods = Unknown = ?
A = amount after n-periods = $5000
We slot the values into the formula. This will be:
A=P(1+i)^n
5000=1347.80(1+.00275)^n
Divide both side by 1347.80
5000/1347.80 = (1.00275)^n
We then take the log of both sides. This will be:
log(5000/1347.80) = nlog(1.00275)
n=log(5000/1347.80)/log(1.00275)
n = 477 months approximately
= 477months/12
= 39 years, 10 months
