Question:
Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7840
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 = $7840 – $4900 = $2940
Thus, Simple Interest = $2940
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 × 2940/4900 × 10
= 294000/49000
= 6 years (using formula)
Thus, Time (T) = 6 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 = $2940 (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 $2940, then the time = 1/490 × 2940 years
= 1 × 2940/490 years
= 2940/490 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.
(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(4) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(6) If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(8) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?