Question:
Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $6674
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 = $6674 – $4700 = $1974
Thus, Simple Interest = $1974
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 × 1974/4700 × 7
= 197400/32900
= 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) = $4700
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $1974 (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 $1974, then the time = 1/329 × 1974 years
= 1 × 1974/329 years
= 1974/329 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(2) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.
(5) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(7) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.
(10) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.