Final answer:
To determine the amount of money Larry will have in the account after 10 years with quarterly compounded interest, we apply the compound interest formula using the given parameters. The formula including the principal, rate, time, and the number of compounding periods per year is used to compute the future value of the investment.
Step-by-step explanation:
The question requires us to calculate the future value of money when $750,000 is invested in a savings account with an interest rate of 3.8% per annum, compounded quarterly, over a period of 10 years.
To find the amount of money that will be in the account after 10 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, 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 in years.
Plugging in the values from the question, we get:
A = 750,000(1 + 0.038/4)^(4*10)
Calculating the values inside the formula, the future value of the investment will be:
A = 750,000(1 + 0.0095)^(40)
A = 750,000(1.0095)^40
After solving, we can find the total amount of money in the savings account once Larry retires.