Answer:
look at the solution
Explanation:
The question is about Jamie wanting to deposit $1000 into a registered retirement savings account. Bank A offers 6% interest compounded monthly, while Bank B offers 7% interest compounded annually.
To determine which option would be more beneficial for Jamie, we need to calculate the amount of money he would have at the end of a specific period of time for each bank.
Let's start with Bank A, which offers 6% interest compounded monthly. The formula to calculate the future value of an investment with compound interest is:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment
P is the principal amount (initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times that interest is compounded per year
t is the number of years the money is invested for
For Bank A, the principal amount (P) is $1000, the annual interest rate (r) is 6% or 0.06 (as a decimal), the number of times interest is compounded per year (n) is 12 (since it's compounded monthly), and the number of years (t) can be any desired period.
Let's say Jamie plans to leave the money in the account for 5 years. Plugging these values into the formula, we get:
A = 1000(1 + 0.06/12)^(12*5)
= 1000(1 + 0.005)^(60)
= 1000(1.005)^(60)
≈ $1338.23
So after 5 years, Jamie would have approximately $1338.23 in Bank A.
Now let's calculate the amount for Bank B, which offers 7% interest compounded annually. Since the interest is compounded annually, we can use the simple interest formula:
A = P(1 + rt)
Where the variables have the same meanings as before.
Using the same values as before, we have:
A = 1000(1 + 0.07*5)
= 1000(1 + 0.35)
= 1000(1.35)
= $1350
So after 5 years, Jamie would have $1350 in Bank B.
Comparing the results, we can see that Bank B offers a higher return on investment than Bank A. After 5 years, Jamie would have $1350 in Bank B compared to $1338.23 in Bank A.
Therefore, if Jamie wants to maximize his investment, Bank B would be the better option.