Question:
Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $12420
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $12420 – $6900 = $5520
Thus, Simple Interest = $5520
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 × 5520/6900 × 10
= 552000/69000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $6900
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5520 (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 $6900
= 10/100 × 6900
= 10 × 6900/100
= 69000/100 = 690
Thus, simple Interest for 1 year = $690
Now,
∵ If the simple Interest is $690, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/690 years
∴ If the simple Interest is $5520, then the time = 1/690 × 5520 years
= 1 × 5520/690 years
= 5520/690 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
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(2) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(3) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.
(4) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?
(7) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 5% simple interest?
(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?