Question:
Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7176
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 = $7176 – $4600 = $2576
Thus, Simple Interest = $2576
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 × 2576/4600 × 8
= 257600/36800
= 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) = $4600
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2576 (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 $2576, then the time = 1/368 × 2576 years
= 1 × 2576/368 years
= 2576/368 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.
(2) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?
(5) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.
(7) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.
(8) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.
(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.