Question:
Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8960
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $8960 – $5600 = $3360
Thus, Simple Interest = $3360
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 × 3360/5600 × 6
= 336000/33600
= 10 years (using formula)
Thus, Time (T) = 10 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) = 6% per annum
Simple Interest = $3360 (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 = 6% of Principal
= 6% of $5600
= 6/100 × 5600
= 6 × 5600/100
= 33600/100 = 336
Thus, simple Interest for 1 year = $336
Now,
∵ If the simple Interest is $336, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/336 years
∴ If the simple Interest is $3360, then the time = 1/336 × 3360 years
= 1 × 3360/336 years
= 3360/336 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(4) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?
(9) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(10) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.