Question:
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.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $6816
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 = $6816 – $4800 = $2016
Thus, Simple Interest = $2016
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 × 2016/4800 × 7
= 201600/33600
= 6 years (using formula)
Thus, Time (T) = 6 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 = $2016 (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 $2016, then the time = 1/336 × 2016 years
= 1 × 2016/336 years
= 2016/336 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.
(3) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 8% simple interest?
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.
(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 10% simple interest?
(10) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.