Question:
Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $11152
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 = $11152 – $6800 = $4352
Thus, Simple Interest = $4352
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 × 4352/6800 × 8
= 435200/54400
= 8 years (using formula)
Thus, Time (T) = 8 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) = 8% per annum
Simple Interest = $4352 (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 = 8% of Principal
= 8% of $6800
= 8/100 × 6800
= 8 × 6800/100
= 54400/100 = 544
Thus, simple Interest for 1 year = $544
Now,
∵ If the simple Interest is $544, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/544 years
∴ If the simple Interest is $4352, then the time = 1/544 × 4352 years
= 1 × 4352/544 years
= 4352/544 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
(3) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 4 years.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.
(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(7) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.