# reverse interest calculator **URL:** \ **Category:** Factual Questions\ **Created:** [March 11, 2004, 1:04am UTC](https://boards.straightdope.com/t/reverse-interest-calculator/233592 "2004-03-11T01:04:11Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![paul\_smars](https://avatars.discourse-cdn.com/v4/letter/p/3be4f8/32.png) [@paul\_smars](https://boards.straightdope.com/u/paul_smars)\ **Post date:** [March 11, 2004, 1:04am UTC](https://boards.straightdope.com/t/reverse-interest-calculator/233592/1 "2004-03-11T01:04:11Z")
I searched but could not find, please help me. I need an on-lline calculator to give me the effective yearly interest earned. I will enter initial dollar amount, dollar amount earned, and term in months. As in $1200, earned $350, and term was 22 months. Thanks, P ---
**Author:** ![Sublight](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@Sublight](https://boards.straightdope.com/u/Sublight)\ **Post date:** [March 11, 2004, 2:14am UTC](https://boards.straightdope.com/t/reverse-interest-calculator/233592/2 "2004-03-11T02:14:03Z")
I couldn’t find one online but if you have a scientific calculator, there’s a fairly easy way to do it yourself. Assuming you’re talking about continuously compounded interest, start with A=Pe[sup]rt[/sup] A is the Amount you have now (in your example, $1550) P is your starting Principle ($1200) e is simply e, which is about 2.7 but you won’t have to worry about that. r is the interest rate (what you want to know) t is the time (22 months) 1. Take the natural log of each side. lnA = lnPe[sup]rt[/sup] 2. Multiplying two numbers is equivalent to adding their logs, so: lnA = lnP + lne[sup]rt[/sup] 3. The natural log of e[sup]x[/sup] is just x (trust me), so: lnA = lnP + rt (remember I said you wouldn’t need to worry about e?) 4. Now just calculate the natural logs (on a scientific calculator it’s the ‘ln’ button) lnA = 7.34601 lnP = 7.09007 and find rt ## 7.34601 - 7.09007 0.25594 = rt Since t = 22 months, divide this number by 22 to get the monthly interest (1.16%) or by (22/12) to get the annual interest (13.96%) Basically, just take the natural log of the current amount and the starting principle, subtract them, and the answer will be equal to the interest rate multiplied by the time. ---
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [March 11, 2004, 2:17am UTC](https://boards.straightdope.com/t/reverse-interest-calculator/233592/3 "2004-03-11T02:17:09Z")
Answer: it depends on how you want to consider the interest compounded. Credit cards compound daily (well, daily based on average daily balance), for example, which does correspond to an APR in terms of DPR\*365. If you want to consider it only compounded yearly, or continuously, the answer is different. Here is a general formula for anything but continuously compounded interest: P = principle F = final total I = 1+R (that is, 1 + PercentageRate/100) t = time compounded I[sup]t[/sup]P = F I’m assuming you want to solve for R = I - 1. Derivation follows: I[sup]t[/sup]P = F I[sup]t[/sup] = F/P t ln(I) = ln(F/P) ln(I) = [ln(F/P)]/t I = e[sup][ln(F/P)]/t[/sup] R = e[sup][ln(F/P)]/t[/sup] - 1 Which I whipped up in an excel spreadsheet. Compounded monthly, your monthly interest rate over 22 months was 0.011701266 or about 1.17%, corresponding to an APR of 14.042%. Compunded yearly: 0.149814099, or about 14.981% APR. Compounded daily: 0.000382539, or about 13.963% APR. ---
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [March 11, 2004, 2:32am UTC](https://boards.straightdope.com/t/reverse-interest-calculator/233592/4 "2004-03-11T02:32:38Z")
Here’s a pretty good compound interest calculator: [http://www.1728.com/compint.htm](http://www.1728.com/compint.htm) You would be solving for RATE The principal is $1200 The years = 1.83333 (22 months) The Total is 1550 (1200 + 350) The answer is 14.98 % (if compounded yearly. If you wanted to convert this to other compounding methods go to: [http://www.1728.com/yieldint.htm](http://www.1728.com/yieldint.htm) Enter 14.98, click “calculate” scroll to section 2 and you will see this equals 14.457454988 Semi-Annually 14.205219656 Quarterly 14.040303859 Monthly 13.961470914 Daily 13.958801421 Continuously The monthly and daily amounts agree with erislover’s calculations. ---
**Author:** ![paul\_smars](https://avatars.discourse-cdn.com/v4/letter/p/3be4f8/32.png) [@paul\_smars](https://boards.straightdope.com/u/paul_smars)\ **Post date:** [March 11, 2004, 7:18am UTC](https://boards.straightdope.com/t/reverse-interest-calculator/233592/5 "2004-03-11T07:18:23Z")
> [@wolf\_meister](#): > > Here’s a pretty good compound interest calculator: > [COMPOUND INTEREST CALCULATOR](http://www.1728.com/compint.htm) > > You would be solving for RATE > > The principal is $1200 > The years = 1.83333 (22 months) > The Total is 1550 (1200 + 350) > > The answer is 14.98 % (if compounded yearly. Thanks all of you. This one is the best. It works without taking my scentific cacu out of the drawer ---
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [March 11, 2004, 2:59pm UTC](https://boards.straightdope.com/t/reverse-interest-calculator/233592/6 "2004-03-11T14:59:40Z")
**Paul** Gee thanks. By the way, that’s my website and I’m glad you like that calculator.