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 $12160 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6400

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

Amount (A) = $12160

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 = $12160 – $6400 = $5760

Thus, Simple Interest = $5760

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 × 5760}/_{6400 × 9}

= ⁵⁷⁶⁰⁰⁰/₅₇₆₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $5760 (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 $5760, then the time = ¹/₅₇₆ × 5760 years

= ^{1 × 5760}/₅₇₆ years

= ⁵⁷⁶⁰/₅₇₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.

(2) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?

(3) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.

(4) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.

(6) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.

(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

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

(10) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?