Question:
David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7152
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 = $7152 – $4800 = $2352
Thus, Simple Interest = $2352
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 × 2352/4800 × 7
= 235200/33600
= 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) = $4800
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2352 (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 = 7% of Principal
= 7% of $4800
= 7/100 × 4800
= 7 × 4800/100
= 33600/100 = 336
Thus, simple Interest for 1 year = $336
Now,
∵ If the simple Interest is $336, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/336 years
∴ If the simple Interest is $2352, then the time = 1/336 × 2352 years
= 1 × 2352/336 years
= 2352/336 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?
(2) 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.
(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(8) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.