Question:
Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $10472
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 = $10472 – $6800 = $3672
Thus, Simple Interest = $3672
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 × 3672/6800 × 6
= 367200/40800
= 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) = $6800
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3672 (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 $6800
= 6/100 × 6800
= 6 × 6800/100
= 40800/100 = 408
Thus, simple Interest for 1 year = $408
Now,
∵ If the simple Interest is $408, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/408 years
∴ If the simple Interest is $3672, then the time = 1/408 × 3672 years
= 1 × 3672/408 years
= 3672/408 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.
(2) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(5) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(7) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.
(10) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.