Question:
Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $8112
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 = $8112 – $5200 = $2912
Thus, Simple Interest = $2912
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 × 2912/5200 × 8
= 291200/41600
= 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) = $5200
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2912 (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 $5200
= 8/100 × 5200
= 8 × 5200/100
= 41600/100 = 416
Thus, simple Interest for 1 year = $416
Now,
∵ If the simple Interest is $416, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/416 years
∴ If the simple Interest is $2912, then the time = 1/416 × 2912 years
= 1 × 2912/416 years
= 2912/416 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
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(2) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(3) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?
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(9) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
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