Question:
Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 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) = 10% per annum
Amount (A) = $11160
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 = $11160 – $6200 = $4960
Thus, Simple Interest = $4960
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 × 4960/6200 × 10
= 496000/62000
= 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) = 10% per annum
Simple Interest = $4960 (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 = 10% of Principal
= 10% of $6200
= 10/100 × 6200
= 10 × 6200/100
= 62000/100 = 620
Thus, simple Interest for 1 year = $620
Now,
∵ If the simple Interest is $620, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/620 years
∴ If the simple Interest is $4960, then the time = 1/620 × 4960 years
= 1 × 4960/620 years
= 4960/620 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(2) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 8% simple interest?
(5) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?
(8) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(9) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.