Question:
Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9800
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 = $9800 – $4900 = $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 × 4900/4900 × 10
= 490000/49000
= 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) = $4900
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 $4900
= 10/100 × 4900
= 10 × 4900/100
= 49000/100 = 490
Thus, simple Interest for 1 year = $490
Now,
∵ If the simple Interest is $490, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/490 years
∴ If the simple Interest is $4900, then the time = 1/490 × 4900 years
= 1 × 4900/490 years
= 4900/490 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?
(3) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(5) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(6) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(7) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.
(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(10) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.