Prop. III.
An Estate being offered for a certain Sum of money, the annual Rent is also known: Q What
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An Estate being offered for a certain Sum of money, the annual Rent is also known: Q What
Rate of Interest upon Interest shall the Pur∣chaser have for his money?
Equation, V ÷ S = R − 1.
The annual Rent being divided by the Sum demanded, quotes the Rate less Unity.
Example.
Quest. 1. There is a Free-hold Estate to be sold for 1600 l. the yearly Rent being 128 l. what Rate of Interest shall the Purchaser have for his money?
〈 math 〉〈 math 〉
Quest. 2. Admit there be a small Farm to be sold of the Value of 35 l. per Annum for 500 l. what Rate of Compound Interest shall the Purchaser have for his money at that price?
〈 math 〉〈 math 〉
Furthermore, if it be inquired how many years Purchase any Annuity is worth, putting R = the Ratio as before, and Y the number of Years, the Rule is: 〈 math 〉〈 math 〉
That is, Divide Unity by the Ratio less 1, and the Quote informs the Number of Years.
Example.
There is a Free-hold Estate to be sold, Q. How many Years Purchase is it worth at 5 per Cent. per Annum?
〈 math 〉〈 math 〉
The Answer is 20 Years Purchase.
What is it worth at 6 per Cent. p••r Annum?
〈 math 〉〈 math 〉
The Answer is 16 Years, and ⅔ of a Year.
Again, if an Estate be offered at any num∣ber of Years Purchase, and it be demanded what Rate of Interest the Purchaser shall have for his Money, the Rule is: 〈 math 〉〈 math 〉
That is, Divide Unity by the number of Years propos'd, and the Quote exhibits the Ratio, less Unity.
Example.
An Estate is offered at 20 Years Purchase, what Rate of Interest shall the Purchaser then have?
〈 math 〉〈 math 〉
The Answer is 5 per Cent. per Annum.