Question:
Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9540
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 = $9540 – $5300 = $4240
Thus, Simple Interest = $4240
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 × 4240/5300 × 10
= 424000/53000
= 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) = $5300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4240 (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 $5300
= 10/100 × 5300
= 10 × 5300/100
= 53000/100 = 530
Thus, simple Interest for 1 year = $530
Now,
∵ If the simple Interest is $530, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/530 years
∴ If the simple Interest is $4240, then the time = 1/530 × 4240 years
= 1 × 4240/530 years
= 4240/530 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?
(3) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?
(6) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(8) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(10) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?