Question : Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
Correct Answer 10
Solution & Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10200
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 = $10200 – $5100 = $5100
Thus, Simple Interest = $5100
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 × 5100/5100 × 10
= 510000/51000
= 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) = $5100
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5100 (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 $5100
= 10/100 × 5100
= 10 × 5100/100
= 51000/100 = 510
Thus, simple Interest for 1 year = $510
Now,
∵ If the simple Interest is $510, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/510 years
∴ If the simple Interest is $5100, then the time = 1/510 × 5100 years
= 1 × 5100/510 years
= 5100/510 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(5) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.
(9) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?