Simple Interest
Math MCQs

Question :    Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6300

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $12600

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 = $12600 – $6300 = $6300

Thus, Simple Interest = $6300

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 × 6300}/_{6300 × 10}

= ⁶³⁰⁰⁰⁰/₆₃₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 10% per annum

Simple Interest = $6300 (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 $6300

= ¹⁰/₁₀₀ × 6300

= ^{10 × 6300}/₁₀₀

= ⁶³⁰⁰⁰/₁₀₀ = 630

Thus, simple Interest for 1 year = $630

Now,

∵ If the simple Interest is $630, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₃₀ years

∴ If the simple Interest is $6300, then the time = ¹/₆₃₀ × 6300 years

= ^{1 × 6300}/₆₃₀ years

= ⁶³⁰⁰/₆₃₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.

(2) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?

(3) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

(5) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(6) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.

(9) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.

(10) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?