Final answer:
After 6 months, there will be $3,817.50 in Jacob's account, which is calculated using the compound interest formula for the principal amount of $3,750, at a semi-annual interest rate of 3.6%.
Step-by-step explanation:
When Jacob deposits $3,750 into an account with a 3.6% interest rate compounded semi-annually, we need to calculate the amount in the account after 6 months. Since the interest is compounded semi-annually, it is compounded twice a year. However, since we are only looking for the amount after 6 months (half a year), we will use the formula for compound interest but only for one period of compounding.
The compound interest formula is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n periods, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In this case, P is $3,750, r is 0.036 (3.6% as a decimal), n is 2 (since the interest is compounded semi-annually), and t is 0.5 (representing 6 months as half a year).
Now, we substitute these values into our formula:
A = $3,750(1 + 0.036/2)^(2*0.5)
A = $3,750(1 + 0.018)^1
A = $3,750(1.018)
A = $3,817.50
So, after 6 months, there will be $3,817.50 in Jacob's account.