Question

g If the interest rate is 5 percent, what is the present value of $10 received one year from now

Answer 1

Given:

Rate of interest = 5%

Amount = $10

Time = 1 year.

To find:

The present value (initial value).

Solution:

Let x be the initial value.

Rate of interest = 5%

So, amount after 1 years is

Amount = Initial value + 5% of initial value

$A=x+\dfrac{5}{100}x$

$10=x+0.05x$

$10=1.05x$

Divide both sides by 1.05.

$\dfrac{10}{1.05}=x$

$9.5238095...=x$

$x\approx 9.52$

Therefore, the present value is about $9.52.

Answer 2

Based on the amount received, the period it is received, and the interest rate, the present value is $9.52.

The present value is calculated as:

= Amount / ( ( 1 + rate) ^ number of periods)

Solving gives:

= 10 / ( 1 + 5%)¹

= 10 / 1.05

= $9.52

In conclusion, the present value is $9.52.

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