Question:
Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8378
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 = $8378 – $5900 = $2478
Thus, Simple Interest = $2478
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 × 2478/5900 × 6
= 247800/35400
= 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) = $5900
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2478 (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 = 6% of Principal
= 6% of $5900
= 6/100 × 5900
= 6 × 5900/100
= 35400/100 = 354
Thus, simple Interest for 1 year = $354
Now,
∵ If the simple Interest is $354, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/354 years
∴ If the simple Interest is $2478, then the time = 1/354 × 2478 years
= 1 × 2478/354 years
= 2478/354 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
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(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.
(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?
(5) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.
(8) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(9) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?
(10) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.