Question:
Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9828
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 = $9828 – $6300 = $3528
Thus, Simple Interest = $3528
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 × 3528/6300 × 7
= 352800/44100
= 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) = $6300
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3528 (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 $6300
= 7/100 × 6300
= 7 × 6300/100
= 44100/100 = 441
Thus, simple Interest for 1 year = $441
Now,
∵ If the simple Interest is $441, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/441 years
∴ If the simple Interest is $3528, then the time = 1/441 × 3528 years
= 1 × 3528/441 years
= 3528/441 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(3) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(5) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?
(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(8) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.
(10) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?