Question:
Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $12350
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 = $12350 – $6500 = $5850
Thus, Simple Interest = $5850
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 × 5850/6500 × 9
= 585000/58500
= 10 years (using formula)
Thus, Time (T) = 10 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) = $6500
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5850 (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 $6500
= 9/100 × 6500
= 9 × 6500/100
= 58500/100 = 585
Thus, simple Interest for 1 year = $585
Now,
∵ If the simple Interest is $585, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/585 years
∴ If the simple Interest is $5850, then the time = 1/585 × 5850 years
= 1 × 5850/585 years
= 5850/585 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.
(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(5) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(10) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.