Question

Find the following values. Compounding/discounting occurs annually. Do not round intermediate calculations. Round your answers to the nearest cent. a. An initial $200 compounded for 10 years at 7%. $   b. An initial $200 compounded for 10 years at 14%. $   c. The present value of $200 due in 10 years at 7%. $   d. The present value of $2,165 due in 10 years at 14% and 7%. Present value at 14%: $   Present value at 7%: $   e. Define present value. 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. 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. 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. 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. 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. -Select-IIIIIIIVVItem 6 How are present values affected by interest rates? Assuming positive interest rates, the present value will increase as the interest rate increases. Assuming positive interest rates, the present value will decrease as the interest rate increases. Assuming positive interest rates, the present value will decrease as the interest rate decreases. Assuming positive interest rates, the present value will not change as the interest rate increases. Assuming positive interest rates, the present value will not change as the interest rate decreases.

Answer 1

Future value is computed as follows:

= Present value x (1 + r)ⁿ

Present value is computed as follows:

= Future value / (1 + r)ⁿ

a. The amount is computed as follows:

= $ 200 x 1.07¹⁰

= $ 200 x 1.967151357

= $ 393.43 Approximately

b. The amount is computed as follows:

= $ 200 x 1.14¹⁰

= $ 200 x 3.707221314

= $ 741.44 Approximately

c. The amount is computed as follows:

= $ 200 / 1.07¹⁰

= $ 200 / 1.967151357

= $ 101.67 Approximately

d. The amount is computed as follows:

= $ 2,165 / 1.14¹⁰

= $ 2,165 / 3.707221314

= $ 584 Approximately

d. The amount is computed as follows:

= $ 2,165 / 1.07¹⁰

= $ 1,100.58 Approximately

e. As we know the present value is computed as follows:

Present value = Future value / (1 + r)ⁿ

So, the correct answer is option of:

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.

f. As we know the present value is computed as follows:

Present value = Future value / (1 + r)ⁿ

So, the correct answer is option of:

Assuming positive interest rates, the present value will decrease as the interest rate increases. Since the denominator in the formula will increase and as a result the numerator will decrease and so does the present value.