Question:
Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11900
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 = $11900 – $7000 = $4900
Thus, Simple Interest = $4900
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 × 4900/7000 × 10
= 490000/70000
= 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) = $7000
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4900 (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 $7000
= 10/100 × 7000
= 10 × 7000/100
= 70000/100 = 700
Thus, simple Interest for 1 year = $700
Now,
∵ If the simple Interest is $700, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/700 years
∴ If the simple Interest is $4900, then the time = 1/700 × 4900 years
= 1 × 4900/700 years
= 4900/700 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
(2) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.
(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.
(6) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(7) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?
(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(9) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(10) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.