Question:
Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10980
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 = $10980 – $6100 = $4880
Thus, Simple Interest = $4880
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 × 4880/6100 × 10
= 488000/61000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $6100
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4880 (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 $6100
= 10/100 × 6100
= 10 × 6100/100
= 61000/100 = 610
Thus, simple Interest for 1 year = $610
Now,
∵ If the simple Interest is $610, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/610 years
∴ If the simple Interest is $4880, then the time = 1/610 × 4880 years
= 1 × 4880/610 years
= 4880/610 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?
(2) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?
(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.