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 $9856 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6400

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

Amount (A) = $9856

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 = $9856 – $6400 = $3456

Thus, Simple Interest = $3456

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 × 3456}/_{6400 × 9}

= ³⁴⁵⁶⁰⁰/₅₇₆₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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 = $3456 (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 $3456, then the time = ¹/₅₇₆ × 3456 years

= ^{1 × 3456}/₅₇₆ years

= ³⁴⁵⁶/₅₇₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?

(2) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(3) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?

(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?

(5) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?

(6) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.

(8) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?

(10) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.