Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6600

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $11220

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 = $11220 – $6600 = $4620

Thus, Simple Interest = $4620

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 × 4620}/_{6600 × 7}

= ⁴⁶²⁰⁰⁰/₄₆₂₀₀

= 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) = $6600

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $4620 (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 = 7% of Principal

= 7% of $6600

= ⁷/₁₀₀ × 6600

= ^{7 × 6600}/₁₀₀

= ⁴⁶²⁰⁰/₁₀₀ = 462

Thus, simple Interest for 1 year = $462

Now,

∵ If the simple Interest is $462, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₂ years

∴ If the simple Interest is $4620, then the time = ¹/₄₆₂ × 4620 years

= ^{1 × 4620}/₄₆₂ years

= ⁴⁶²⁰/₄₆₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?

(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.

(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?

(4) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.

(6) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?

(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.

(8) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?

(9) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?

(10) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?