Question:
Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9387
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 = $9387 – $6300 = $3087
Thus, Simple Interest = $3087
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 × 3087/6300 × 7
= 308700/44100
= 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) = $6300
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3087 (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 $6300
= 7/100 × 6300
= 7 × 6300/100
= 44100/100 = 441
Thus, simple Interest for 1 year = $441
Now,
∵ If the simple Interest is $441, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/441 years
∴ If the simple Interest is $3087, then the time = 1/441 × 3087 years
= 1 × 3087/441 years
= 3087/441 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?
(2) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
(4) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(6) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.
(8) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
(9) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?