Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6600

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $10560

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 = $10560 – $6600 = $3960

Thus, Simple Interest = $3960

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 × 3960}/_{6600 × 10}

= ³⁹⁶⁰⁰⁰/₆₆₀₀₀

= 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) = $6600

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3960 (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 $6600

= ¹⁰/₁₀₀ × 6600

= ^{10 × 6600}/₁₀₀

= ⁶⁶⁰⁰⁰/₁₀₀ = 660

Thus, simple Interest for 1 year = $660

Now,

∵ If the simple Interest is $660, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₆₀ years

∴ If the simple Interest is $3960, then the time = ¹/₆₆₀ × 3960 years

= ^{1 × 3960}/₆₆₀ years

= ³⁹⁶⁰/₆₆₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?

(5) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?

(6) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?

(8) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.

(9) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

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