Question:
Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $6560
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 = $6560 – $4100 = $2460
Thus, Simple Interest = $2460
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 × 2460/4100 × 10
= 246000/41000
= 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) = $4100
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $2460 (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 = 10% of Principal
= 10% of $4100
= 10/100 × 4100
= 10 × 4100/100
= 41000/100 = 410
Thus, simple Interest for 1 year = $410
Now,
∵ If the simple Interest is $410, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/410 years
∴ If the simple Interest is $2460, then the time = 1/410 × 2460 years
= 1 × 2460/410 years
= 2460/410 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
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(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(3) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
(5) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(6) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(9) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
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