Question:
Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10988
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 = $10988 – $6700 = $4288
Thus, Simple Interest = $4288
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 × 4288/6700 × 8
= 428800/53600
= 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) = $6700
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4288 (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 = 8% of Principal
= 8% of $6700
= 8/100 × 6700
= 8 × 6700/100
= 53600/100 = 536
Thus, simple Interest for 1 year = $536
Now,
∵ If the simple Interest is $536, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/536 years
∴ If the simple Interest is $4288, then the time = 1/536 × 4288 years
= 1 × 4288/536 years
= 4288/536 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(3) How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?
(4) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(6) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(8) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.