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) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(3) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.
(5) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?
(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?
(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.