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 $11970 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6300

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

Amount (A) = $11970

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 = $11970 – $6300 = $5670

Thus, Simple Interest = $5670

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 × 5670}/_{6300 × 10}

= ⁵⁶⁷⁰⁰⁰/₆₃₀₀₀

= 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) = $6300

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

Simple Interest = $5670 (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 $5670, then the time = ¹/₆₃₀ × 5670 years

= ^{1 × 5670}/₆₃₀ years

= ⁵⁶⁷⁰/₆₃₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.

(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?

(4) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(5) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(7) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(8) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?

(10) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.