Question:
John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7480
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 = $7480 – $4400 = $3080
Thus, Simple Interest = $3080
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 × 3080/4400 × 7
= 308000/30800
= 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) = $4400
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3080 (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 = 7% of Principal
= 7% of $4400
= 7/100 × 4400
= 7 × 4400/100
= 30800/100 = 308
Thus, simple Interest for 1 year = $308
Now,
∵ If the simple Interest is $308, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/308 years
∴ If the simple Interest is $3080, then the time = 1/308 × 3080 years
= 1 × 3080/308 years
= 3080/308 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?
(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(5) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(6) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(8) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
(10) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.