Question:
Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 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) = 6% per annum
Amount (A) = $6532
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 = $6532 – $4600 = $1932
Thus, Simple Interest = $1932
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 × 1932/4600 × 6
= 193200/27600
= 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) = 6% per annum
Simple Interest = $1932 (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 $4600
= 6/100 × 4600
= 6 × 4600/100
= 27600/100 = 276
Thus, simple Interest for 1 year = $276
Now,
∵ If the simple Interest is $276, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/276 years
∴ If the simple Interest is $1932, then the time = 1/276 × 1932 years
= 1 × 1932/276 years
= 1932/276 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?
(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(3) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.
(7) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.
(9) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(10) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.