Simple Interest
Math MCQs

Question :    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.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6400

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $11008

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 = $11008 – $6400 = $4608

Thus, Simple Interest = $4608

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 × 4608}/_{6400 × 9}

= ⁴⁶⁰⁸⁰⁰/₅₇₆₀₀

= 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) = $6400

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4608 (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 $6400

= ⁹/₁₀₀ × 6400

= ^{9 × 6400}/₁₀₀

= ⁵⁷⁶⁰⁰/₁₀₀ = 576

Thus, simple Interest for 1 year = $576

Now,

∵ If the simple Interest is $576, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₇₆ years

∴ If the simple Interest is $4608, then the time = ¹/₅₇₆ × 4608 years

= ^{1 × 4608}/₅₇₆ years

= ⁴⁶⁰⁸/₅₇₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(2) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.

(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(4) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.

(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.

(8) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?

(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?

(10) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?