Question:
Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7384
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 = $7384 – $5200 = $2184
Thus, Simple Interest = $2184
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 × 2184/5200 × 7
= 218400/36400
= 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) = $5200
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2184 (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 $5200
= 7/100 × 5200
= 7 × 5200/100
= 36400/100 = 364
Thus, simple Interest for 1 year = $364
Now,
∵ If the simple Interest is $364, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/364 years
∴ If the simple Interest is $2184, then the time = 1/364 × 2184 years
= 1 × 2184/364 years
= 2184/364 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) If Mary borrowed $3050 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?
(3) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(7) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.
(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.