Q1) An inventor has been offered $12,000 per year for the next 5 years and $6000 annually for the following 7 years for the exclusive rights to an invention. At what price could the inventor afford to sell the rights to earn 10 percent, disregarding taxes.
My attempt:
The first portion on finds the present worth for annuity, then second portion finds the present worth of an annuity but then since this is 5 years in the future, we must consider that a future worth and multiply by another factor get its present worth.
Is this correct?
Q2) A company borrowed $100,000 to finance a new product. The loan was for 20 years at a nominal interest rate of 8 percent compounded semiannually. It was to be repaid in 40 equal payments. After one half of the payments were made, the company decided to pay the remaining balance in one final payment at the end of the 10th year. How much was owed?
My attempt:
So in 20 payments he would have paid,
What is the total future worth (all 40 payments) of his 100k loan?
Once he has made half the payments, how much is the present worth of his loan?
Therefore,
Ah of course, this is an obvious mistake thank you!
If there are 40 equal payments in 20 years, I would assume that it would be semiannually because,What is frequency of payments: monthly, semiannually or anually?
You should realise that balance owing will certainly not be > 100,000
2*20 = 40 payments
Hence why I used an interest rate of 4% and not 8% in all my calculations.
I can't see why it's obvious to conclude that the balance owed is going to be less than 100,000. Could you explain why?
Correct; payment is semiannual, and 4% is used to calculate the interest at each payment.
Balance MUST be less than 100,000, else loan would never get repaid; think about it!
Required semiannual payment: 100000(.04) / (1 - 1/1.04^40) = 5052.3489....so $5,052.35
Here's what the loan "looks like" as it gets repaid:
********** this is amount required to pay off loan after 20 payments; OK?Code:N PAYMENT INTEREST BALANCE 0 100,000.00 1 -5,052.35 4,000.00 98,947.65 2 -5,052.35 3,957.91 96,714.21 ..... 20 -5,052.35 2,835.21 68,663.07 ********** ..... 39 -5,052.35 381.17 4,858.03 40 -5,052.35 194.32 .00
This amount can be calculated by formula:
future value of 100000.00 over 20 periods less future value of 20 payments of 5052.35; here:
100000(1.04^20) = 219112.31 [1]
5052.35(1.04^20 - 1) / .04 = 150449.24 [2]
[1] - [2] = 68663.07
So, you all ok now?
NO. That's the FUTURE VALUE
Present value would be 56923.02 / 1.10^7 = 29210.51Code:0 .00 1 6000.00 6000.00 2 6000.00 600.00 12600.00 3 6000.00 1260.00 19860.00 ... 7 6000.00 4629.37 56923.02
TRY and get this straight:
first, the $6000 flow is discounted to 29210.51; that's its value end of year 5;
then the 29210.51 is discounted to TODAY: 29210.51 / 1.10^5 = 18137.43