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 6 years if he takes a loan of $3700 at 2% simple interest?

(2) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.

(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.

(5) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.

(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.

(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 3 years.

(10) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.