Q7.5 B9

In this question you know the present value of two payments which you are going to have to make in the future. The total is 1100. You are going to have to make two equal payments, one in 4 months and another in 6 months. Interest is 8.5%. Two things: you know the present value of two payments which are in the future, so we use the present value formula P = S/(1 + rt). AND since the two payments are the same, we can call each payment 'x'.

So...

1100 = x/(1+ 0.085*4/12) + x/(1 + 0.085*6/12)
1100 = x/1.0283 + x/1.0425
1100 = 0.972 x + 0.959 x
1100 = 1.932 x
x = 1100/1.932 = 569.36

Note that my answer is slightly different from the book's answer just because of rounding.

Think through this problem carefully and make sure you 'get it'. Working out whether an interest problem is 'future value' or 'present value' isn't easy. So work at it. Example 7.5 H covers the same ground as the question above.

When there's no selling price

Sometimes the selling price isn’t provided. In these cases, assume that the selling price is $1 per unit. So in the case of the question below from the quiz:
(Chapter 6 quiz Q4) Monk Foods has compiled these estimates for operations:
Sales 865,000
Fixed costs 252,100
Total variable cost 597,250
The margin is 865000 – 597250 = 267750. Now we calculate the margin per dollar of sales. Divide the margin by the total sales: 267750/865000 = 0.31. That means for every dollar in sales, we get to keep 31 cents to use to pay off the fixed costs. So how many units do we need to sell at $1 each to pay off the fixed costs of 252,100?
252,100/0.31 = 813,225.8. Now, in units we would want to round UP to 813,226. For amount of sales required to break even, leave the amount at 813,225.8.

See Example 6.18 on page 234 of the textbook.

Partial payments

Sometimes we can’t settle a complete invoice, but we can pay at least some of it and can get a discount for what we do pay. In the Quiz on Chapter 5, there is a question on this. Basically, how much do you need to pay to reduce an invoice of 9600 to 7000. So, we want the creditor (the company you owe money to) to record a payment of 2600. But your partial payment occurs within the discount period. So you don’t have to pay the full 2600. You pay less. The 2600 is the ‘amount given credit for’. The discount is 5%. So we take off 5% from what we want to have appear in the creditor company accounts. That’s 0.95*2600 = 2470. So you pay the creditor 2470 but they record your payment as being 2600. The textbook (8th edition) has a good example on page 193.

Q5.4 B8

Here is the solution to Q5.4 B8.

First, calculate the full cost, meaning what the folks would have paid if they didn't have the discount. That is 225 + 2 x 12 + .75 x 2 x 20 = 279

Now, the package was sold at the discounted price of 199. So the markdown was 279 - 199 = 80.

The rate of markdown was 80/279 = 28.67%

Points to note: the rate of markdown is calculated based on the list price.

The Nalini word problem

Here is the question: Nalini invested a total of $24,000 in two mutual funds. Her investment in the Equity Fund is $4000 less than three times her investment in the Bond Fund. How much did Nalini invest in the Equity Fund?

Solution: first, assign a letter to each of the unknown quantities. We have two unknown quantities, let's call the Equity Fund 'E' and the Bond Fund 'B'. Now, because we have two unknown quantities, we will need two equation to find them.

First off, her investment is E + B = 24000. That is from the first sentence.

Now,  the tougher second sentence. Recall that the point of an equation is that both sides must be equal. So, we can write

E = 3B - 4000

Go  back to our first equation. Because an equation is...well....an equation, we can substitute
the rearranged second equation for E into the first equation to get

3B - 4000 + B = 24000 ( make sure you get this bit)

so 4B = 28000
so B = 7000

We can get E like this

E + 7000 = 24000, so E = 17000.

Check your work. Go back to the sentence "Her investment in the Equity Fund is $4000 less than three times her investment in the Bond Fund". Three times the Bond Fund would be 3 * 7 = 21000. Take away 4000 to get 21000 - 4000 = 17000. We're done!