Question:
Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $12127
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 = $12127 – $6700 = $5427
Thus, Simple Interest = $5427
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 × 5427/6700 × 9
= 542700/60300
= 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) = $6700
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5427 (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 = 9% of Principal
= 9% of $6700
= 9/100 × 6700
= 9 × 6700/100
= 60300/100 = 603
Thus, simple Interest for 1 year = $603
Now,
∵ If the simple Interest is $603, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/603 years
∴ If the simple Interest is $5427, then the time = 1/603 × 5427 years
= 1 × 5427/603 years
= 5427/603 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(2) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(4) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?
(5) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
(7) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.
(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?
(9) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(10) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.