Question:
Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7544
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 = $7544 – $4600 = $2944
Thus, Simple Interest = $2944
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 × 2944/4600 × 8
= 294400/36800
= 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) = $4600
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2944 (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 $4600
= 8/100 × 4600
= 8 × 4600/100
= 36800/100 = 368
Thus, simple Interest for 1 year = $368
Now,
∵ If the simple Interest is $368, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/368 years
∴ If the simple Interest is $2944, then the time = 1/368 × 2944 years
= 1 × 2944/368 years
= 2944/368 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.
(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?
(3) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.
(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?
(9) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.