Question:
Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9180
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 = $9180 – $5100 = $4080
Thus, Simple Interest = $4080
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 × 4080/5100 × 10
= 408000/51000
= 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) = $5100
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4080 (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 $5100
= 10/100 × 5100
= 10 × 5100/100
= 51000/100 = 510
Thus, simple Interest for 1 year = $510
Now,
∵ If the simple Interest is $510, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/510 years
∴ If the simple Interest is $4080, then the time = 1/510 × 4080 years
= 1 × 4080/510 years
= 4080/510 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(3) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(5) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
(6) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(8) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?
(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.