Question:
Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9372
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 = $9372 – $6600 = $2772
Thus, Simple Interest = $2772
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 × 2772/6600 × 6
= 277200/39600
= 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) = $6600
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2772 (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 $6600
= 6/100 × 6600
= 6 × 6600/100
= 39600/100 = 396
Thus, simple Interest for 1 year = $396
Now,
∵ If the simple Interest is $396, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/396 years
∴ If the simple Interest is $2772, then the time = 1/396 × 2772 years
= 1 × 2772/396 years
= 2772/396 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?
(3) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(4) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?
(7) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(8) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(9) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(10) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.