Question:
Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9840
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 = $9840 – $6000 = $3840
Thus, Simple Interest = $3840
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 × 3840/6000 × 8
= 384000/48000
= 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) = $6000
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3840 (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 $6000
= 8/100 × 6000
= 8 × 6000/100
= 48000/100 = 480
Thus, simple Interest for 1 year = $480
Now,
∵ If the simple Interest is $480, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/480 years
∴ If the simple Interest is $3840, then the time = 1/480 × 3840 years
= 1 × 3840/480 years
= 3840/480 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(3) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(7) What amount will be due after 2 years if David borrowed a sum of $3200 at a 6% simple interest?
(8) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.
(9) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(10) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.