Question:
Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10140
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $10140 – $6500 = $3640
Thus, Simple Interest = $3640
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 × 3640/6500 × 8
= 364000/52000
= 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) = $6500
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3640 (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 $6500
= 8/100 × 6500
= 8 × 6500/100
= 52000/100 = 520
Thus, simple Interest for 1 year = $520
Now,
∵ If the simple Interest is $520, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/520 years
∴ If the simple Interest is $3640, then the time = 1/520 × 3640 years
= 1 × 3640/520 years
= 3640/520 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(2) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?
(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(6) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(7) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?
(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.