Question:
Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8313
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 = $8313 – $5100 = $3213
Thus, Simple Interest = $3213
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 × 3213/5100 × 7
= 321300/35700
= 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) = $5100
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3213 (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 $5100
= 7/100 × 5100
= 7 × 5100/100
= 35700/100 = 357
Thus, simple Interest for 1 year = $357
Now,
∵ If the simple Interest is $357, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/357 years
∴ If the simple Interest is $3213, then the time = 1/357 × 3213 years
= 1 × 3213/357 years
= 3213/357 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
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(2) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(3) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(5) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.
(6) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?
(7) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(8) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?
(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.