Question

Find the following values. Compounding/discounting occurs annually. Do not round intermediate calculations. Round your answers to the nearest cent.

(a) An initial $300 compounded for 10 years at 9%.
(b) An initial $300 compounded for 10 years at 18%.
(c) The present value of $300 due in 10 years at 9%.
(d) The present value of $1,085 due in 10 years at 18% and 9%. Present value at 18%:$ Present value at 9%:$
(e) Define present value.
I. The present value is the value today of a sum of money to be received in the future and in general is less than the future value.
II. The present value is the value today of a sum of money to be received in the future and in general is greater than the future value.
III. The present value is the value today of a sum of money to be received in the future and in general is equal to the future value.
IV. The present value is the value in the future of a sum of money to be received today and in general is less than the future value.
V. The present value is the value in the future of a sum of money to be received today and in general is greater than the future value. How are present values affected by interest rates?

Answer 1

(a) $644.49, (b) $1,542.63, (c) $122.13, (d) Present value at 18%: $347.73, Present value at 9%: $400.65.

(e) The present value is defined as the current worth of a future sum of money, and it generally decreases as interest rates rise.

Step-by-step explanation:

(a) The future value (FV) is calculated using the formula
`FV = PV * (1 + r)^n,`where PV is the present value, r is the interest rate, and n is the number of compounding periods. For (a), $300 compounded for 10 years at 9% annually gives $644.49.

(b) Similarly, for (b), the future value is $1,542.63, as it is compounded at a higher rate of 18% annually.

(c) To find the present value (PV) in (c), we use the formula
`PV = FV / (1 + r)^n.`The present value of $300 due in 10 years at 9% is $122.13.

(d) For (d), we calculate the present values at both 18% and 9%. At 18%, the present value is $347.73, and at 9%, it is $400.65.

(e) Present values are inversely affected by interest rates. As interest rates increase, the present value decreases because the opportunity cost of not having the money invested at a higher rate is greater. Therefore, the present value is lower when discounted at higher interest rates.