Simple Interest
Math MCQs

Question :    David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4800

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $7824

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 = $7824 – $4800 = $3024

Thus, Simple Interest = $3024

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 × 3024}/_{4800 × 9}

= ³⁰²⁴⁰⁰/₄₃₂₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $4800

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3024 (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 = 9% of Principal

= 9% of $4800

= ⁹/₁₀₀ × 4800

= ^{9 × 4800}/₁₀₀

= ⁴³²⁰⁰/₁₀₀ = 432

Thus, simple Interest for 1 year = $432

Now,

∵ If the simple Interest is $432, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₂ years

∴ If the simple Interest is $3024, then the time = ¹/₄₃₂ × 3024 years

= ^{1 × 3024}/₄₃₂ years

= ³⁰²⁴/₄₃₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.

(2) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.

(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(5) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.

(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?

(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.