Mike has 700 dollars in a bank account. The bank account earns 4.5% interest, compounded annually.
a) Write an equation that models this situation
b) How much interest will have Jerome have earned in 10 years?
4.5% = 4.5/100 = .045
That means you add .045 times the amount present every year.
That is, for the first year, you get 700 + 700 * .045 = 700(1+.045) = 700*1.045
and you multiply by that every year.
After t years, the amount in the account will be
700*1.045^t
So just plug in t=10 and subtract the original 700 to find the interest earned
700(1.045^10 - 1) = 387.08
Where did you get 1.045?
a) To model this situation, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount after t years
P is the principal amount (initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, Mike has $700 in the bank account, the interest rate is 4.5% (or 0.045 as a decimal), and the interest is compounded annually.
Therefore, the equation that models this situation is:
A = 700(1 + 0.045/1)^(1* t)
b) To find out how much interest Jerome will have earned in 10 years, we need to calculate the difference between the final amount (A) and the initial deposit (P).
Using the equation from part a:
A = 700(1 + 0.045/1)^(1 * 10)
A = 700(1 + 0.045)^(10)
A ≈ 700(1.045)^10
A ≈ 700(1.522)
A ≈ 1065.40
To find the interest earned, we subtract the initial deposit from the final amount:
Interest = A - P
Interest = 1065.40 - 700
Interest ≈ 365.40
Therefore, Jerome will have earned approximately $365.40 in interest after 10 years.