Question:
Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9672
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 = $9672 – $6200 = $3472
Thus, Simple Interest = $3472
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 × 3472/6200 × 7
= 347200/43400
= 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) = $6200
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3472 (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 = 7% of Principal
= 7% of $6200
= 7/100 × 6200
= 7 × 6200/100
= 43400/100 = 434
Thus, simple Interest for 1 year = $434
Now,
∵ If the simple Interest is $434, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/434 years
∴ If the simple Interest is $3472, then the time = 1/434 × 3472 years
= 1 × 3472/434 years
= 3472/434 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(2) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(3) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?
(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(7) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.
(9) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.