Question : Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
Correct Answer 10
Solution & Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9400
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $9400 – $4700 = $4700
Thus, Simple Interest = $4700
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 × 4700/4700 × 10
= 470000/47000
= 10 years (using formula)
Thus, Time (T) = 10 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) = $4700
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4700 (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 $4700
= 10/100 × 4700
= 10 × 4700/100
= 47000/100 = 470
Thus, simple Interest for 1 year = $470
Now,
∵ If the simple Interest is $470, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/470 years
∴ If the simple Interest is $4700, then the time = 1/470 × 4700 years
= 1 × 4700/470 years
= 4700/470 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?