Final answer:
Mayer Company will receive the initial deposit plus compound interest earned over 12 years at a 4% annual rate. The compound interest formula is A = P(1 + r/n)^(nt), and by plugging in the given values, we can calculate the total amount that will be received at the end of the lease period.
Step-by-step explanation:
The question asks how much money Mayer Company will receive at the end of a 12-year lease period with a security deposit of $9,200 made at the start of the lease. The deposit will earn interest compounded annually at a rate of 4%. To calculate the future value of the deposit, we can use the formula for compound interest: 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 the money is invested for, in years.
In this case, P = $9,200, r = 0.04 (4% converted to a decimal), n = 1 (since interest is compounded annually), and t = 12 (12 years). So, the calculation is:
A = $9,200 * (1 + 0.04/1)^(1*12)
A = $9,200 * (1 + 0.04)^12
A = $9,200 * 1.04^12
By calculating the value of 1.04 raised to the 12th power and multiplying it by $9,200, we find the total amount that Mayer Company will receive at the end of the lease, which includes the principal and the interest earned over the 12 years.