Question:
Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9089 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9089
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 = $9089 – $6100 = $2989
Thus, Simple Interest = $2989
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 × 2989/6100 × 7
= 298900/42700
= 7 years (using formula)
Thus, Time (T) = 7 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) = 7% per annum
Simple Interest = $2989 (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 = 7% of Principal
= 7% of $6100
= 7/100 × 6100
= 7 × 6100/100
= 42700/100 = 427
Thus, simple Interest for 1 year = $427
Now,
∵ If the simple Interest is $427, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/427 years
∴ If the simple Interest is $2989, then the time = 1/427 × 2989 years
= 1 × 2989/427 years
= 2989/427 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?
(3) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?
(8) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?
(10) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.