Question:
Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9856
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 = $9856 – $6400 = $3456
Thus, Simple Interest = $3456
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 × 3456/6400 × 6
= 345600/38400
= 9 years (using formula)
Thus, Time (T) = 9 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) = $6400
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3456 (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 = 6% of Principal
= 6% of $6400
= 6/100 × 6400
= 6 × 6400/100
= 38400/100 = 384
Thus, simple Interest for 1 year = $384
Now,
∵ If the simple Interest is $384, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/384 years
∴ If the simple Interest is $3456, then the time = 1/384 × 3456 years
= 1 × 3456/384 years
= 3456/384 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(4) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 4 years.
(7) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(8) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?