Question:
Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8976
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 = $8976 – $6600 = $2376
Thus, Simple Interest = $2376
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 × 2376/6600 × 6
= 237600/39600
= 6 years (using formula)
Thus, Time (T) = 6 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 = $2376 (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 $2376, then the time = 1/396 × 2376 years
= 1 × 2376/396 years
= 2376/396 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.
(2) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 4 years.
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.
(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?
(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(10) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?