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) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?

(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?

(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?

(6) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?

(7) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?

(9) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.