Present Value (Interest)

Question

The question goes like this:

What deposit made today will provide for a payment of 1000 in 1 year and 2,000 in 3 years, if the effective rate of interest is 7.5%? The answer given by the book is 2540 which resulted by adding the present value of 1000 and 2000.

(1000(1+0.075)^-1)+(2000(1+0.075)^-3)= 2540. It's just I don't get it, can someone explain this to me? How come that you just add the present values of the two?

My answer is 679.68 which come from subtracting the two present values. I believe my way of thinking in this problem is not right.

Answer 1

It's just I don't get it, can someone explain this to me? How come that you just add the present values of the two?

Because the reference date has to be the same on both sides of the equation. The deposit is made today.

$\text{deposit value (today)}=\text{sum of the present values of the payments }$

$x= \frac{1000}{(1+0.075)^1}+\frac{2000}{(1+0.075)^3}$

Answer 2

$$\left[2540\times1.075-1000\right]\times1.075^{2}=1999,8\approx2000$$

After a year you have $2540\times1.075$ on the bank. That capital is diminished with $1000$ (the payment). The rest stands for $2$ years and grows to $2000$ that is payed at the end of $3$ years.

Actually to be solved is the equation:$$\left[x\times1.075-1000\right]\times1.075^{2}=2000$$