Question:
Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 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) = 9% per annum
Amount (A) = $7783
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 = $7783 – $4300 = $3483
Thus, Simple Interest = $3483
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 × 3483/4300 × 9
= 348300/38700
= 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) = 9% per annum
Simple Interest = $3483 (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 $3483, then the time = 1/387 × 3483 years
= 1 × 3483/387 years
= 3483/387 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.
(2) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(3) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(5) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.
(6) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) 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.
(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 10% simple interest?
(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?