Question:
Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6724 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $6724
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 = $6724 – $4100 = $2624
Thus, Simple Interest = $2624
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 × 2624/4100 × 8
= 262400/32800
= 8 years (using formula)
Thus, Time (T) = 8 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) = $4100
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2624 (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 = 8% of Principal
= 8% of $4100
= 8/100 × 4100
= 8 × 4100/100
= 32800/100 = 328
Thus, simple Interest for 1 year = $328
Now,
∵ If the simple Interest is $328, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/328 years
∴ If the simple Interest is $2624, then the time = 1/328 × 2624 years
= 1 × 2624/328 years
= 2624/328 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?
(3) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.
(4) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(9) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.