Question

$1,000 received 5 years from today discounted at an annual rate of 10% has a smaller present value than $1,000 received 10 years from today discounted at an annual rate of 5%. Is it true or false?

Answer 1

A) $1,000 received 5 years from today @ 10% annual rate.

Future value is given i.e., $1,000

Interest rate = 10%

Number of years = 5 years.

We know that, Future value = present value * ( 1 + r% )ⁿ

Therefore, Present value = Future value / ( 1 + r% )ⁿ

Present value, here = 1000 / (1+0.1)⁵ = 1000 / 1.61 = $620.92

B) $1,000 received 10 years from today @ 5%

Future value = $1,000

Number of years = 10 years

Interest rate = 5%

Therefore, present value = 1,000 / (1+0.05)¹⁰ = 1000 / 1.63 = $613.91

Therefore, false as A has higher present value ($620) than that of B ($614).