Simple Interest
Math MCQs

Question :    Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6300

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $10332

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 = $10332 – $6300 = $4032

Thus, Simple Interest = $4032

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 × 4032}/_{6300 × 8}

= ⁴⁰³²⁰⁰/₅₀₄₀₀

= 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) = 8% per annum

Simple Interest = $4032 (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 = 8% of Principal

= 8% of $6300

= ⁸/₁₀₀ × 6300

= ^{8 × 6300}/₁₀₀

= ⁵⁰⁴⁰⁰/₁₀₀ = 504

Thus, simple Interest for 1 year = $504

Now,

∵ If the simple Interest is $504, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₀₄ years

∴ If the simple Interest is $4032, then the time = ¹/₅₀₄ × 4032 years

= ^{1 × 4032}/₅₀₄ years

= ⁴⁰³²/₅₀₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.

(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.

(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?

(5) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?

(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.

(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?

(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.

(9) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.