I am stumped on the below - hopefully someone better than me at math can explain.
The effective annual interest rate for a nominal interest rate of 10% compounded monthly is equal to the below: = (1 + (10% / 12)) ^ 12 - 1
= 10.47%
So, assuming a $100 single capital contribution, total annual accrued interest is $10.47 in year 1 assuming no payments. How do you back into the daily compounded rate that will produce total annual interest of 10.47% or the same total pref amount of $10.47 off the same contribution?
General Formula: [1 + (i / n)] ^ n -1 Where: i = annual rate, n = number of compounding periods (i.e. months, days, etc.)
Given total effective annual rate of 10.47%:
0.1047 = (1 + i / 365) ^ 365 - 1
1.1047 = (1 + i / 365) ^ 365
1.1047 ^ (1 / 365) = 1 + i / 365
1.1047 ^ (1 / 365) - 1 = i / 365
[1.1047 ^ (1 / 365) - 1] * 365 = i = 0.099587
Thanks for the reply. Let me further clarify, I need the rate below (i) that would result in $10.47 of total interest after Day 365.
Day 0 - $100 contribution Day 1 - $100 * (1+i) = a Day 2 - a * (1+i) = b Day 3 - b * (1+i) = c etc...
That's what I gave you.
i = 0.099587, or 9.96%
That rate doesn't work when the cumulative accrued interest is compounded daily.
Saepe ducimus voluptatem quibusdam quo et similique voluptas. Amet eaque cumque deleniti. Corrupti quia voluptatem iste at voluptatum quis.
Ad magnam corrupti quia voluptas et quibusdam. Autem excepturi nobis similique itaque iure deserunt atque repellendus. Ut eum quos aut debitis laborum animi voluptates.
Eius quis voluptas eum debitis fuga nesciunt. Accusamus est accusantium non cupiditate. Consequatur nobis et omnis maiores voluptates adipisci harum ut. Rerum non saepe eaque sunt. Beatae dolorem earum ratione est qui. Et tempora molestias et ut.
Voluptas animi voluptatem itaque molestiae tempore rerum corrupti. Odio quia accusantium velit reiciendis veniam corrupti perspiciatis. Magni et sapiente molestiae consectetur sit expedita.
See All Comments - 100% Free
WSO depends on everyone being able to pitch in when they know something. Unlock with your email and get bonus: 6 financial modeling lessons free ($199 value)
or Unlock with your social account...