Question:
Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8313
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 = $8313 – $5100 = $3213
Thus, Simple Interest = $3213
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 × 3213/5100 × 9
= 321300/45900
= 7 years (using formula)
Thus, Time (T) = 7 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 = $3213 (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 $3213, then the time = 1/459 × 3213 years
= 1 × 3213/459 years
= 3213/459 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
(2) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?
(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.
(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 2% simple interest?
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.
(8) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?
(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?