Question:
Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9128
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 = $9128 – $5600 = $3528
Thus, Simple Interest = $3528
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 × 3528/5600 × 9
= 352800/50400
= 7 years (using formula)
Thus, Time (T) = 7 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) = $5600
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3528 (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 = 9% of Principal
= 9% of $5600
= 9/100 × 5600
= 9 × 5600/100
= 50400/100 = 504
Thus, simple Interest for 1 year = $504
Now,
∵ If the simple Interest is $504, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/504 years
∴ If the simple Interest is $3528, then the time = 1/504 × 3528 years
= 1 × 3528/504 years
= 3528/504 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(2) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
(3) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(6) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.
(8) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(9) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.