Question:
Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7003
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 = $7003 – $4700 = $2303
Thus, Simple Interest = $2303
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 × 2303/4700 × 7
= 230300/32900
= 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) = $4700
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2303 (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 $4700
= 7/100 × 4700
= 7 × 4700/100
= 32900/100 = 329
Thus, simple Interest for 1 year = $329
Now,
∵ If the simple Interest is $329, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/329 years
∴ If the simple Interest is $2303, then the time = 1/329 × 2303 years
= 1 × 2303/329 years
= 2303/329 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(2) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?
(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?