Simple Interest
MCQs Math

Question:     Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $6600

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $11880

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 = $11880 – $6600 = $5280

Thus, Simple Interest = $5280

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 × 5280}/_{6600 × 8}

= ⁵²⁸⁰⁰⁰/₅₂₈₀₀

= 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) = 8% per annum

Simple Interest = $5280 (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 = 8% of Principal

= 8% of $6600

= ⁸/₁₀₀ × 6600

= ^{8 × 6600}/₁₀₀

= ⁵²⁸⁰⁰/₁₀₀ = 528

Thus, simple Interest for 1 year = $528

Now,

∵ If the simple Interest is $528, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₈ years

∴ If the simple Interest is $5280, then the time = ¹/₅₂₈ × 5280 years

= ^{1 × 5280}/₅₂₈ years

= ⁵²⁸⁰/₅₂₈ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.

(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.

(3) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.

(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 8% simple interest.

(5) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?

(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.

(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.

(9) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.