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) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?
(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(5) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(7) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(8) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.