Question:
Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 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) = 7% per annum
Amount (A) = $6854
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 = $6854 – $4600 = $2254
Thus, Simple Interest = $2254
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 × 2254/4600 × 7
= 225400/32200
= 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) = 7% per annum
Simple Interest = $2254 (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 $2254, then the time = 1/322 × 2254 years
= 1 × 2254/322 years
= 2254/322 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(3) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.
(4) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(6) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?
(8) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.
(9) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(10) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.