Question:
Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11946
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 = $11946 – $6600 = $5346
Thus, Simple Interest = $5346
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 × 5346/6600 × 9
= 534600/59400
= 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) = $6600
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5346 (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 = 9% of Principal
= 9% of $6600
= 9/100 × 6600
= 9 × 6600/100
= 59400/100 = 594
Thus, simple Interest for 1 year = $594
Now,
∵ If the simple Interest is $594, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/594 years
∴ If the simple Interest is $5346, then the time = 1/594 × 5346 years
= 1 × 5346/594 years
= 5346/594 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(2) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 5% simple interest?
(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(4) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(5) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?
(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(8) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.
(10) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.