Question:
Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9231
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 = $9231 – $5100 = $4131
Thus, Simple Interest = $4131
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 × 4131/5100 × 9
= 413100/45900
= 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) = $5100
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4131 (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 $5100
= 9/100 × 5100
= 9 × 5100/100
= 45900/100 = 459
Thus, simple Interest for 1 year = $459
Now,
∵ If the simple Interest is $459, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/459 years
∴ If the simple Interest is $4131, then the time = 1/459 × 4131 years
= 1 × 4131/459 years
= 4131/459 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?
(3) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(5) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(8) Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(10) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 7% simple interest?