Final answer:
Using the compound interest formula, you can calculate the future value of a $16,000 deposit at a 4.7% annual interest rate after 5 years. For the present value of a security that pays $20,000 in 10 years at a 7.6% discount rate, the present value formula is applied.
Step-by-step explanation:
To calculate how much would be in your account after 5 years with an initial deposit of $16,000 at an annual interest rate of 4.7%, you can use the formula for compound interest, which is 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, and t is the time the money is invested for in years. Assuming the interest is compounded annually (n = 1), the calculation would be as follows:
A = $16,000(1 + 0.047/1)^(1\*5)
This simplifies to:
A = $16,000(1 + 0.047)^5
For the present value of a security that will pay $20,000 in 10 years with an annual discount rate of 7.6%, you use the present value formula, which is PV = FV / (1 + r/n)^(nt), where PV is the present value, FV is the future value, r is the annual discount rate (decimal), n is the number of times the discount rate is compounded per year, and t is the time in years until the future value is received. In this case, the calculation would be:
PV = $20,000 / (1 + 0.076/1)^(1\*10)