Question:
Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8008
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 = $8008 – $5200 = $2808
Thus, Simple Interest = $2808
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 × 2808/5200 × 9
= 280800/46800
= 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) = $5200
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $2808 (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 = 9% of Principal
= 9% of $5200
= 9/100 × 5200
= 9 × 5200/100
= 46800/100 = 468
Thus, simple Interest for 1 year = $468
Now,
∵ If the simple Interest is $468, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/468 years
∴ If the simple Interest is $2808, then the time = 1/468 × 2808 years
= 1 × 2808/468 years
= 2808/468 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.
(3) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
(4) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.
(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?