Question:
Michael took a loan of $4600 at the rate of 7% 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
8
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 7% 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 × 7
= 257600/32200
= 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) = 7% 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 = 7% of Principal
= 7% of $4600
= 7/100 × 4600
= 7 × 4600/100
= 32200/100 = 322
Thus, simple Interest for 1 year = $322
Now,
∵ If the simple Interest is $322, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/322 years
∴ If the simple Interest is $2576, then the time = 1/322 × 2576 years
= 1 × 2576/322 years
= 2576/322 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.
(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(4) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.
(5) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(6) 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.
(7) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.
(9) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.