Question:
Daniel took a loan of $6200 at the rate of 10% 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
9
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 10% 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 × 10
= 558000/62000
= 9 years (using formula)
Thus, Time (T) = 9 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) = 10% 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 = 10% of Principal
= 10% of $6200
= 10/100 × 6200
= 10 × 6200/100
= 62000/100 = 620
Thus, simple Interest for 1 year = $620
Now,
∵ If the simple Interest is $620, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/620 years
∴ If the simple Interest is $5580, then the time = 1/620 × 5580 years
= 1 × 5580/620 years
= 5580/620 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(3) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(9) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(10) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?