“I see.”
“If you spend the interest, that is calledsimple interest.However, if you justleave it there, you roll the interest over. The next year you would earn 4% on £104—the original £100 plus the £4 from last year. You would get, let us see—£4 3s. Then youroll that over as well, and the next year you make the interest on £108 3s. It grows and grows. The longer you leave it, the faster it grows. Look at this.”
Elizabeth pulled out the paper she had used with Mr Collins. “This is important for you to understand, though I will always be around to assist. I assumed you would save £400 per annum. You may or may not contrive it; it may be more one year and less another, but you get the idea. I stretched the number to the limit, but the principle is the same even with a smaller amount.”
She pointed to the relevant line on the paper.
£400 per annum × 20 years at 4% = £12,000
“During these 20 years, you contribute only£8,000—simple multiplication—yes?”
Mary seemed to follow well enough, so Elizabeth continued.
“However, you earn £4,000 morefor doingabsolutely nothingbut letting the Crown use your money. Think of it, Mary! Your tiny little parsonage, saving a large but manageable amount, would earn as much as Longbourn’s income for 6 years—all by refraining from wasting money.”
Mary stared at the numbers for several yards, and finally asked, “What about with, say, 25 years?”
Elizabeth laughed, pulled out a pencil, turned the paper over, and wrote:
Payment x (((1 + r) n)—1)
r
She pointed at the formula.
“ris the interest rate as a decimal, so 4% is .04.nis the number of years. Parentheses group quantities, so you start in the centre and work your way out.”
Mary nodded, though she was unlikely to have understood.
“It is difficult to calculate the power without a log table or slide rule[ii], but I already calculated 20 years, I can easily add 5 more by common arithmetic. I calculate the interest each year by multiplication and keep a running sum. It is not in the least elegant, but I can do it here.”
Elizabeth used a fallen log as a table, performed the calculations quickly, and answered, “£16,500.”
Mary stared at the numbers in consternation and drew the obvious conclusion. “Let us say I had the unbelievably bad luck to bear 5 daughters while my indolent husband blundered along for 25 years. You say I could have a£3,000dowry for each of my daughterson a clergyman’s living.”
Elizabeth nodded sympathetically. “Hence Uncle Gardiner’s cursing, which was admittedly impressive. It gets even worse.”
Mary’s eyebrows shot up to her hairline. “Worse than our father, who graduated from Cambridge with honours, with an income of £2,000, failing tomatch the savings of a clergyman with £600 being advised by a 20-year-old woman who has never been within a mile of a school of any sort?”
Elizabeth sighed. “That is bad enough, but consider this. You know Mama has a £5,000 jointure?”
“She constantly grumbles that she will starve in the hedgerows if that is all she has to live on, as if it were not her own fault.”
“Remember the lesson in compound interest. It is calculated with a simple formula, though it is, again, difficult to do without a log table or a slide rule. I was fortunate when I spoke with Mr Collins, as I had a sailor’s navigation book full of log tables in the parlour purely by chance.”
Elizabeth added the formula to the back of the paper.
P (1+r) n
“P is theprincipal: the amount you start with—£5,000 in this case—nis the number of periods—25 years. It is easy with the right tools, but difficult in your head. Fortunately, I calculated it the day after Uncle Gardiner’s last tirade, so I happen to know the answer. For the last 25 years, Mama has drawn off the£200 per annumof interest and spent it on entertainment and fripperies.”
Mary nodded.
“First, she can live perfectly well on £200, so there will be no hedgerows anyway,even if she continued spending frivolously and saved nothing. She would live in a home like Aunt Philips’, so most of her whining is overwrought nonsense.”
Elizabeth paused for Mary to acknowledge what was only common sense and simple arithmetic.
“Even worse, had Mama simply refrained from wasting that interest on things we did not need, and Longbourn could well afford anyway, she would have over£13,000now. We have therule of 72. Divide 72 by the percent interest, and that is how many years it takes to double. In the four percents, your money doubles every 18 years. Had she left it alone, she would have £400 per annum to live on, perfectly enough to live much as she does now. She could also have redirected the £200 to Uncle Gardiner, and he would have made an even higher return on it. £15,000 or more lay well within her reach, with no effort whatsoever. And she still probably has 20 years to save even more.”
