Question:
Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9028
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 = $9028 – $6100 = $2928
Thus, Simple Interest = $2928
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 × 2928/6100 × 8
= 292800/48800
= 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) = $6100
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2928 (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 $6100
= 8/100 × 6100
= 8 × 6100/100
= 48800/100 = 488
Thus, simple Interest for 1 year = $488
Now,
∵ If the simple Interest is $488, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/488 years
∴ If the simple Interest is $2928, then the time = 1/488 × 2928 years
= 1 × 2928/488 years
= 2928/488 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
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(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.
(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(5) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(8) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?
(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?