Question:
Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11780
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $11780 – $6200 = $5580
Thus, Simple Interest = $5580
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 5580/6200 × 9
= 558000/55800
= 10 years (using formula)
Thus, Time (T) = 10 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $6200
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5580 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 9% of Principal
= 9% of $6200
= 9/100 × 6200
= 9 × 6200/100
= 55800/100 = 558
Thus, simple Interest for 1 year = $558
Now,
∵ If the simple Interest is $558, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/558 years
∴ If the simple Interest is $5580, then the time = 1/558 × 5580 years
= 1 × 5580/558 years
= 5580/558 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.
(5) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?
(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(7) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.
(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.