Question:
Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 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) = 6% per annum
Amount (A) = $6808
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 = $6808 – $4600 = $2208
Thus, Simple Interest = $2208
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 × 2208/4600 × 6
= 220800/27600
= 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) = 6% per annum
Simple Interest = $2208 (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 $2208, then the time = 1/276 × 2208 years
= 1 × 2208/276 years
= 2208/276 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(3) If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(5) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.
(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 2% simple interest?
(8) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.