Question:
Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6560
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 = $6560 – $4100 = $2460
Thus, Simple Interest = $2460
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 × 2460/4100 × 6
= 246000/24600
= 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) = $4100
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2460 (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 = 6% of Principal
= 6% of $4100
= 6/100 × 4100
= 6 × 4100/100
= 24600/100 = 246
Thus, simple Interest for 1 year = $246
Now,
∵ If the simple Interest is $246, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/246 years
∴ If the simple Interest is $2460, then the time = 1/246 × 2460 years
= 1 × 2460/246 years
= 2460/246 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(4) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.
(7) 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.
(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.
(10) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.