Question:
Patricia took a loan of $4300 at the rate of 6% 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
9
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 6% 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 × 6
= 232200/25800
= 9 years (using formula)
Thus, Time (T) = 9 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) = 6% 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 = 6% of Principal
= 6% of $4300
= 6/100 × 4300
= 6 × 4300/100
= 25800/100 = 258
Thus, simple Interest for 1 year = $258
Now,
∵ If the simple Interest is $258, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/258 years
∴ If the simple Interest is $2322, then the time = 1/258 × 2322 years
= 1 × 2322/258 years
= 2322/258 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?
(6) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(10) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.