Math Question and Answers


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 168189 by mathls last updated on 05/Apr/22

Commented by mathls last updated on 05/Apr/22

$p l e a s e h e l p m e!$
Commented by mr W last updated on 05/Apr/22

$\approx 534 %$
Commented by mr W last updated on 06/Apr/22

$t w o y e a r s = 24 m o n t h e s$ $1 + q_{2 y} = {(1 + q_{m})}^{24}$ $\Rightarrow q_{2 y} = {(1 + q_{m})}^{24} - 1$ $\Rightarrow q_{m} = {(1 + q_{2 y})}^{\frac{1}{24}} - 1$
Commented by mathls last updated on 06/Apr/22

$p l e a s e d e s c r i b e t h e f o r m u l a a n d$ $c a l c u l a t e t h e l a s t a n s b y f o r m u l a .$
Commented by MJS_new last updated on 06/Apr/22

$8 % \to factor 1 + \frac{8}{100} = 1.08$ $1 . 08^{24} = 6.3411 . . . = 1 + \frac{534}{100} \to 534 %$
Commented by mathls last updated on 06/Apr/22

$w h a t m e a n s 534 % ?$
Commented by MJS_new last updated on 06/Apr/22

$534 percent$
Commented by mathls last updated on 07/Apr/22

$p e r c e n t a g e m u s t 100 % b u t i t i s 534 % ?$
Commented by MJS_new last updated on 07/Apr/22

$percentage can be more than 100 %$ $if you need 120 $ to buy something but you$ $only have 60 $ than you have 100 \times \frac{60}{120} % =$ $= 50 % of the price . but if you have 180 $ you$ $have 100 \times \frac{180}{120} % = 150 % of it .$ $if you put all your money on your bank$ $account you put 100 % of your money there .$ $if you get 5 % per year (tell me the name of$ $the bank) you have 105 % of what you had$ $before after the first year (= 100 \times 1.05)$ $if you leave it there another year you have$ $100 \times 1.05 \times 1.05 = 110 . 25 % of what you had$ $before . after n years you have 100 \times 1 . 05^{n} %$ $of what you had in the beginning . after 48$ $years you have 1040 %$
Commented by mathls last updated on 07/Apr/22

$t h a n k s$
Commented by mathls last updated on 08/Apr/22

$p l e a s e p r o v e m e b o t h f o r m u l a .$
	Answered by mr W last updated on 08/Apr/22

	$q_{m} = r a t e p e r m o n t h$ $t h a t m e a n s i f y o u h a v e m o n e y o f$ $a m o u n t A i n t h i s m o n t h, n e x t m o n t h$ $i t b e c o m e s q_{m} A \underset{―}{m o r e}, i . e . n e x t m o n t h$ $y o u t o t a l l y h a v e m o n e y o f a m o u n t$ $A + q_{m} A = (1 + q_{m}) A .$ $s i m i l a r l y a f t e r t w o m o n t h e s {y o u}^{'} l l$ $h a v e {(1 + q_{m})}^{2} A, a n d a f t e r n m o n t h e s$ ${y o u}^{'} l l h a v e {(1 + q_{m})}^{n} A .$ $a f t e r t w o y e a r s, i . e . a f t e r 24 m o n t h e s,$ ${y o u}^{'} l l h a v e {(1 + q_{m})}^{24} A .$ $q_{2 y} = r a t e p e r 2 y e a r s$ $t h a t m e a n s i f y o u h a v e m o n e y o f$ $a m o u n t A i n t h i s m o n t h, a f t e r 2 y e a r s$ $i t b e c o m e s q_{2 y} A m o r e, i . e . a f t e r 2 y e a r s$ ${y o u}^{'} l l h a v e t o t a l l y A + q_{2 y} A = (1 + q_{2 y}) A .$ $w e s e e$ $(1 + q_{2 y}) A = {(1 + q_{m})}^{24} A$ $1 + q_{2 y} = {(1 + q_{m})}^{24}$ $\Rightarrow q_{2 y} = {(1 + q_{m})}^{24} - 1 . . . (I)$ $o r$ $1 + q_{m} = {(1 + q_{2 y})}^{\frac{1}{24}}$ $\Rightarrow q_{m} = {(1 + q_{2 y})}^{\frac{1}{24}} - 1 . . . (I I)$ $e x a m p l e s :$ $g i v e n : m o n t h l y r a t e q_{m} = 8 % = 0.08$ $r a t e p e r 2 y e a r s :$ $q_{2 y} = {(1 + q_{m})}^{24} - 1$ $= {(1 + 0.08)}^{24} - 1$ $\approx 5.34 = 534 %$ $g i v e n : r a t e p e r 2 y e a r s q_{2 y} = 18 % = 0.18$ $m o n t h l y r a t e :$ $q_{m} = {(1 + q_{2 y})}^{\frac{1}{24}} - 1$ $= {(1 + 0.18)}^{\frac{1}{24}} - 1$ $\approx 0.0069 = 0 . 69 %$
	Commented by mathls last updated on 08/Apr/22

	$w h a t a g r e a t s o l u t i o n! u a r e a s t a r o f$ $m a t h e m a t i c s .$
	Commented by peter frank last updated on 08/Apr/22

	$thank you$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum