Question:
Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10608
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 = $10608 – $6800 = $3808
Thus, Simple Interest = $3808
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 × 3808/6800 × 8
= 380800/54400
= 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) = $6800
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3808 (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 $3808, then the time = 1/544 × 3808 years
= 1 × 3808/544 years
= 3808/544 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?
(3) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?
(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(8) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(10) If Kimberly paid $5394 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.