Read time: 1 min OR Video time: 2 mins. Solving Time: 8 mins
Lesson Objective
To learn the formula tying P, r%, n and EMI for the case of SI
#1.
If it is a case of SI, the instalment amount can be found as:
$$ \text{EMI} = \frac{ P \times \left( 1 + r \% \times n \right) }{n \;+\; r \% \times \frac{\left(n-1\right)\times n}{2}} $$
If the question gives us the debt value i.e. the amount owed as on the last date of instalments, then the formula changes to:
$$ \text{EMI} = \frac{ D }{n \;+\; r \% \times \frac{\left(n-1\right)\times n}{2}} $$
Lets use this in the following examples:
E.g. 1
Rs. 2,25,000 is taken as loan at 10% p.a. simple interest. The loan is completely repaid with 6 equal annual instalments, paid at end of each successive year. Find the instalment amount, in Rs.
Answer
Rs. 48,000
Hint
Plug the given data i.e. P = 225000, r% = 1/10, n = 6 in \( \text{EMI} = \frac{ P \times \left( 1 + r \% \times n \right) }{n \;+\; r \% \times \frac{\left(n-1\right)\times n}{2}} \) to find the EMI amount.
Explanation
\( \text{EMI} = \frac{ 225000 \times \left( 1 + \frac{1}{10} \times 6 \right) }{6 \;+\; \frac{1}{10} \times \frac{5 \times 6}{2}} \)
\( \text{EMI} = \frac{ 225000 \times \frac{8}{5} }{\frac{15}{2}} \)
\( \text{EMI} = 225000 \times \frac{8}{5} \times \frac{2}{15} \)
EMI = 3000 × 16 = 48,000
E.g. 2
What equal annual installments, paid at end of each successive year from now, will discharge a debt of Rs. 2,36,000 due in 4 years from now, if rate of interest is 12% p.a. simple interest.
Answer
Rs. 50,000
Hint
Note that Rs. 2,36,000 is due 4 years from now i.e. D, and not P = 236000.
Plug the given data i.e. D = 236000, r% = 12/100 = 3/25, n = 4 in \( \text{EMI} = \frac{ D }{n \;+\; r \% \times \frac{\left(n-1\right)\times n}{2}} \) to find the EMI amount.
Explanation
\( \text{EMI} = \frac{ 236000 }{4 \;+\; \frac{3}{25} \times \frac{3 \times 4}{2}} \)
\( \text{EMI} = \frac{ 236000 }{ \frac{118}{25}} \)
\( \text{EMI} = 236000 \times \frac{25}{118} = 50000\)
E.g. 3
A mobile phone worth Rs. 80,200 is available for Rs. 15,000 downpayment and 4 equal monthly instalments (emi), to be paid at end of each successive month. Find the emi amount if rate of interest is 15% p.a. simple interest.
Answer
Rs. 16,800
Hint #1
Please notice that the given rate is 15% per annum whereas it is a case of monthly instalments. Thus r% will not be 15%.
Hint #2
This is a case of monthly instalments. Thus, we need to use the rate per month, whereas the given rate is 15% per annum. Converting this rate to per month rate, \(r\% = \frac{15}{12} \times \frac{1}{100} = \frac{1}{80} \)
Also the loan value here is not 80,200 but because a down-payment of Rs. 15000 is already done, the loan amount is just 80200 − 15000 = 65200.
Plug P = 65200, r% = 1/80, n = 4 in \( \text{EMI} = \frac{ P \times \left( 1 + r \% \times n \right) }{n \;+\; r \% \times \frac{\left(n-1\right)\times n}{2}} \) to find the EMI amount.
Explanation
\( \text{EMI} = \frac{ 65200 \times \left( 1 + \frac{1}{80} \times 4 \right) }{4 \;+\; \frac{1}{80} \times \frac{3 \times 4}{2}} \)
\( \text{EMI} = \frac{ 65200 \times \frac{21}{20} }{\frac{163}{40}} \)
\( \text{EMI} = 65200 \times \frac{21}{20} \times \frac{40}{163} \)
163 × 4 = 652 and hence EMI = 400 × 21 × 2 = 16,800