Question:
Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $6622
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 = $6622 – $4300 = $2322
Thus, Simple Interest = $2322
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 × 2322/4300 × 9
= 232200/38700
= 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) = $4300
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $2322 (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 = 9% of Principal
= 9% of $4300
= 9/100 × 4300
= 9 × 4300/100
= 38700/100 = 387
Thus, simple Interest for 1 year = $387
Now,
∵ If the simple Interest is $387, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/387 years
∴ If the simple Interest is $2322, then the time = 1/387 × 2322 years
= 1 × 2322/387 years
= 2322/387 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?
(6) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.
(9) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(10) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?