Simple Interest
Math MCQs

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 & 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 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 = $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) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.

(2) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.

(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.

(4) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(5) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.

(7) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.

(9) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

(10) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.