Question:
Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $8288
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 = $8288 – $5600 = $2688
Thus, Simple Interest = $2688
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 × 2688/5600 × 8
= 268800/44800
= 6 years (using formula)
Thus, Time (T) = 6 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) = 8% per annum
Simple Interest = $2688 (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 = 8% of Principal
= 8% of $5600
= 8/100 × 5600
= 8 × 5600/100
= 44800/100 = 448
Thus, simple Interest for 1 year = $448
Now,
∵ If the simple Interest is $448, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/448 years
∴ If the simple Interest is $2688, then the time = 1/448 × 2688 years
= 1 × 2688/448 years
= 2688/448 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(4) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(7) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.