Question 11 (3 points) Odessa deposited S1 347.80 into a savings account with an interest rate of 33% compounded monthly. About how long will it take for the account to be worth

$5,000? (3 points)

O a

Ob

25 years, 5 months

9 years, 5 months

40 years, 5 months

39 years, 10 months

Ос

Od

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

it’s great

Step-by-step explanation: