Question:
Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11900
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 = $11900 – $7000 = $4900
Thus, Simple Interest = $4900
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 × 4900/7000 × 10
= 490000/70000
= 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) = $7000
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4900 (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 = 10% of Principal
= 10% of $7000
= 10/100 × 7000
= 10 × 7000/100
= 70000/100 = 700
Thus, simple Interest for 1 year = $700
Now,
∵ If the simple Interest is $700, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/700 years
∴ If the simple Interest is $4900, then the time = 1/700 × 4900 years
= 1 × 4900/700 years
= 4900/700 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.
(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(7) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?
(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.