given a loan from a bank on a fixed interest rate 5% suppose i want to make monthly payments for 14months how do i calculate the amount i should pay monthly and how do i know how much i will pay back to the bank at the end of the 14months? please i need explanations.


Question and Answers Forum

All Questions Topic List
None Questions
Previous in All Question Next in All Question
Previous in None Next in None
Question Number 165404 by MWSuSon last updated on 01/Feb/22

$given a loan from a bank on a fixed interest rate 5 %$ $suppose i want to make monthly payments for 14 months$ $how do i calculate the amount i should pay monthly and$ $how do i know how much i will pay back to the bank at the$ $end of the 14 months ?$ $please i need explanations .$
Commented by mr W last updated on 01/Feb/22

$n o t o n l y t h e i n t e r e s t r a t e b u t a l s o t h e$ $m o n t h l y p a y m e n t m u s t b e a r r a n g e d$ $w i t h t h e b a n k .$
Commented by MWSuSon last updated on 01/Feb/22

$So {there}^{'} s no way to know how much money {you}^{'} ll pay$ $monthly from the interest rate, loan money and Time to$ $complete payment ?$
Commented by mr W last updated on 01/Feb/22

$i f t h e t i m e t o p a y b a c k t h e c o m p l e t e$ $m o n e y i n c l . i n t e r e s t i s a r r a n g e d,$ $t h e n t h e m o n t h l y p a y m e n t (u s u a l l y$ $a f i x e d a m o u n t) i s a l s o d e t e r m i n e d .$
Commented by mr W last updated on 01/Feb/22

$A = y o u r l o a n$ $p = a n n u a l i n t e r e s t r a t e$ $\frac{p}{12} = p^{'} = m o n t h l y i n t e r e s t r a t e$ $l e t q = 1 + \frac{p}{12} = 1 + p^{'}$ $M = m o n t h l y p a y m e n t (f i x e d a m o u n t)$ $a f t e r 1 m o n t h :$ $i n t e r e s t : A \times \frac{p}{12}$ $y o u o w e d t h e b a n k : A + A \times \frac{p}{12} = q A$ $y o u r p a y m e n t : M$ $y o u s t i l l o w e t h e b a n k : q A - M$ $a f t e r 2 m o n t h e s :$ $i n t e r e s t : (q A - M) \times \frac{p}{12}$ $y o u o w e d t h e b a n k : (q A - M) q$ $y o u r p a y m e n t : M$ $y o u s t i l l o w e t h e b a n k : (q A - M) q - M$ $y o u c a n c o u n t i n u e f u r t h e r .$ $g e n e r a l l y a f t e r n m o n t h e s :$ $y o u s t i l l o w e t h e b a n k :$ ${A q}^{n} - M (1 + q + q^{2} + . . + q^{n - 1})$ $= {A q}^{n} - \frac{M (q^{n} - 1)}{q - 1}$ $s u c h t h a t y o u {d o n}^{'} t o w e t h e b a n k a n y$ $m o n e y a f t e r n m o n t h e s,$ ${A q}^{n} - \frac{M (q^{n} - 1)}{q - 1} = 0$ $\Rightarrow M = \frac{(q - 1) q^{n} A}{q^{n} - 1}$ $e x a m p l e :$ $y o u l o a n 1000 $ f r o m t h e b a n k w i t h$ $a n a n n u a l i n t e r e s t r a t e 6 % .$ $y o u m u s t p a y b a c k c o m p l e t e l y i n$ $20 m o n t h e s .$ $A = 1000 $$ $p = 6 %$ $q = 1 + \frac{p}{12} = 1.005$ $t h e m o n t h l y p a y m e n t i s t h e n$ $M = \frac{0.005 \times 1 . 005^{20} \times 1000}{1 . 005^{20} - 1} \approx 52 . 67 $$ $y o u p a y e d t h e b a n k t o t a l l y$ $20 \times 52.67 = 1053 . 40 $$ $f o r a l o a n o f 1000 $ .$
Commented by mr W last updated on 01/Feb/22

$M = \frac{(q - 1) q^{n} A}{q^{n} - 1} = \frac{p^{'} {(1 + p^{'})}^{n} A}{{(1 + p^{'})}^{n} - 1}$ $\approx \frac{p^{'} (1 + {n p}^{'}) A}{{n p}^{'}} = (\frac{1}{n} + p^{'}) A$
Commented by MWSuSon last updated on 03/Feb/22

$Sorry sir that it took me this long to reply, i do not know why$ $i do not recieve notifications .$ $I just have one question sir, what does q stand for and why$ $is it 1 + \frac{p}{12} ?$
Commented by mr W last updated on 03/Feb/22

$a l l i s e x p l a i n e d :$ $p = a n n u a l i n t e r e s t r a t e$ $\frac{p}{12} = m o n t h l y i n t e r e s t r a t e$ $l e t q = 1 + \frac{p}{12},$ $t h a t m e a n s q s t a n d s f o r 1 + \frac{p}{12} .$ $t h e m e a n i n g o f q i s c l e a r . i t i s t h e$ $c o m m o n r a t i o o f t h e g e o m e t r i c$ $p r o g r e s s i o n . w h e n y o u o w e t h e$ $b a n k m o n e y o f a m o u n t A, o n e$ $m o n t h l a t e r y o u o w e t h e b a n k q A,$ $t w o m o n t h e s l a t e r y o u o w e t h e$ $b a n k q^{2} A, t h r e e m o n t h e s l a t e r y o u$ $o w e q^{3} A, e t c .$
Commented by MWSuSon last updated on 07/Feb/22

$Thank you sir . you really helped me .$
Commented by mr W last updated on 07/Feb/22

$n i c e t o k n o w t h a t!$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum