Question:
Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9983
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 = $9983 – $6700 = $3283
Thus, Simple Interest = $3283
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 × 3283/6700 × 7
= 328300/46900
= 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) = $6700
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3283 (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 $6700
= 7/100 × 6700
= 7 × 6700/100
= 46900/100 = 469
Thus, simple Interest for 1 year = $469
Now,
∵ If the simple Interest is $469, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/469 years
∴ If the simple Interest is $3283, then the time = 1/469 × 3283 years
= 1 × 3283/469 years
= 3283/469 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(4) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.