Question:
Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9520
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 = $9520 – $5600 = $3920
Thus, Simple Interest = $3920
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 × 3920/5600 × 10
= 392000/56000
= 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) = $5600
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3920 (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 $5600
= 10/100 × 5600
= 10 × 5600/100
= 56000/100 = 560
Thus, simple Interest for 1 year = $560
Now,
∵ If the simple Interest is $560, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/560 years
∴ If the simple Interest is $3920, then the time = 1/560 × 3920 years
= 1 × 3920/560 years
= 3920/560 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(2) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 10% simple interest?
(4) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?
(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(8) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(10) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?