Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 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) = 9% per annum

Amount (A) = $11524

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 = $11524 – $6700 = $4824

Thus, Simple Interest = $4824

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 × 4824}/_{6700 × 9}

= ⁴⁸²⁴⁰⁰/₆₀₃₀₀

= 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) = 9% per annum

Simple Interest = $4824 (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 = 9% of Principal

= 9% of $6700

= ⁹/₁₀₀ × 6700

= ^{9 × 6700}/₁₀₀

= ⁶⁰³⁰⁰/₁₀₀ = 603

Thus, simple Interest for 1 year = $603

Now,

∵ If the simple Interest is $603, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₀₃ years

∴ If the simple Interest is $4824, then the time = ¹/₆₀₃ × 4824 years

= ^{1 × 4824}/₆₀₃ years

= ⁴⁸²⁴/₆₀₃ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?

(3) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(6) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.

(8) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.