Question:
Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9943
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 = $9943 – $6100 = $3843
Thus, Simple Interest = $3843
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 × 3843/6100 × 7
= 384300/42700
= 9 years (using formula)
Thus, Time (T) = 9 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) = 7% per annum
Simple Interest = $3843 (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 = 7% of Principal
= 7% of $6100
= 7/100 × 6100
= 7 × 6100/100
= 42700/100 = 427
Thus, simple Interest for 1 year = $427
Now,
∵ If the simple Interest is $427, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/427 years
∴ If the simple Interest is $3843, then the time = 1/427 × 3843 years
= 1 × 3843/427 years
= 3843/427 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
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(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.
(3) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(6) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(7) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.
(9) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 4% simple interest?