Question:
Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9940
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 = $9940 – $7000 = $2940
Thus, Simple Interest = $2940
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 × 2940/7000 × 6
= 294000/42000
= 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) = $7000
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2940 (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 $7000
= 6/100 × 7000
= 6 × 7000/100
= 42000/100 = 420
Thus, simple Interest for 1 year = $420
Now,
∵ If the simple Interest is $420, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/420 years
∴ If the simple Interest is $2940, then the time = 1/420 × 2940 years
= 1 × 2940/420 years
= 2940/420 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
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(2) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.
(4) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(5) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 3 years.
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(8) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.
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