Simple Interest
Math MCQs

Question :    Matthew took a loan of $6400 at the rate of 10% 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  9

Solution & Explanation

Solution

Given,

Principal (P) = $6400

Rate of Simple Interest (R) = 10% 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 × 10}

= ⁵⁷⁶⁰⁰⁰/₆₄₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = 10% 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 = 10% of Principal

= 10% of $6400

= ¹⁰/₁₀₀ × 6400

= ^{10 × 6400}/₁₀₀

= ⁶⁴⁰⁰⁰/₁₀₀ = 640

Thus, simple Interest for 1 year = $640

Now,

∵ If the simple Interest is $640, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₄₀ years

∴ If the simple Interest is $5760, then the time = ¹/₆₄₀ × 5760 years

= ^{1 × 5760}/₆₄₀ years

= ⁵⁷⁶⁰/₆₄₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?

(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?

(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?

(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?

(6) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.

(8) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?

(10) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.