Langstraat was seventeen when he purchased a motorcycle. when applying for insurance,

d) increases as the interest rate decreases.

Explanation:

Present value is the value today; future value is the value some time in the future.

The mere notion of the value of money in time should tell you that, further away in time (towards the future) a sum of money is found, the lower its value today.

Then, you should be able to rule out some propositions that are contrary to that intuition:

a) decreases as the time period decreases ↔ clearly false: the present value increases as the time period decreasese) is directly related to the time period. ↔ clearly false: the present value is inversely related to the time period.

How is the present value related to the future value?

They are directly related: the higher a lump sum in the future the higher the value of it in the present; more money is more money always. More money in the future has more value in the present; less money in the future has less value in the present. Thus,  the option b). is inversely related to the future value is false

How is the present value related to the interest rate?. Which one is true?

c) is directly related to the interest rate, ord) increases as the interest rate decreases

The present value is calculated discounted the future value at the interest rate. The interest rate is in the denominator of the equation to pass from future value to present value. Thus, they are inversely related (c is false); the less the interest rate, the higher the present value of a future amount (confirm d is true).

Therefore, the correct answer is that the present of a lump sum future amount: d) increases as the interest rate decreases.