Question:
Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10064
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 = $10064 – $6800 = $3264
Thus, Simple Interest = $3264
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 × 3264/6800 × 8
= 326400/54400
= 6 years (using formula)
Thus, Time (T) = 6 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 = $3264 (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 $3264, then the time = 1/544 × 3264 years
= 1 × 3264/544 years
= 3264/544 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?
(2) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.
(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(4) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(6) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?
(7) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(9) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.