Question:
Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $8550
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 = $8550 – $4500 = $4050
Thus, Simple Interest = $4050
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 × 4050/4500 × 10
= 405000/45000
= 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) = $4500
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4050 (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 = 10% of Principal
= 10% of $4500
= 10/100 × 4500
= 10 × 4500/100
= 45000/100 = 450
Thus, simple Interest for 1 year = $450
Now,
∵ If the simple Interest is $450, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/450 years
∴ If the simple Interest is $4050, then the time = 1/450 × 4050 years
= 1 × 4050/450 years
= 4050/450 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
(2) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(4) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.
(6) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?
(8) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
(10) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.