Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6700

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $10452

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 = $10452 – $6700 = $3752

Thus, Simple Interest = $3752

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 × 3752}/_{6700 × 7}

= ³⁷⁵²⁰⁰/₄₆₉₀₀

= 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) = $6700

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3752 (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 $6700

= ⁷/₁₀₀ × 6700

= ^{7 × 6700}/₁₀₀

= ⁴⁶⁹⁰⁰/₁₀₀ = 469

Thus, simple Interest for 1 year = $469

Now,

∵ If the simple Interest is $469, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₉ years

∴ If the simple Interest is $3752, then the time = ¹/₄₆₉ × 3752 years

= ^{1 × 3752}/₄₆₉ years

= ³⁷⁵²/₄₆₉ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.

(2) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?

(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.

(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.

(8) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) 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.