Simple Interest
Math MCQs

Question :    David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4800

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7104

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 = $7104 – $4800 = $2304

Thus, Simple Interest = $2304

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 × 2304}/_{4800 × 6}

= ²³⁰⁴⁰⁰/₂₈₈₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 6% per annum

Simple Interest = $2304 (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 = 6% of Principal

= 6% of $4800

= ⁶/₁₀₀ × 4800

= ^{6 × 4800}/₁₀₀

= ²⁸⁸⁰⁰/₁₀₀ = 288

Thus, simple Interest for 1 year = $288

Now,

∵ If the simple Interest is $288, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₈ years

∴ If the simple Interest is $2304, then the time = ¹/₂₈₈ × 2304 years

= ^{1 × 2304}/₂₈₈ years

= ²³⁰⁴/₂₈₈ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?

(2) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(3) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?

(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.

(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?

(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.

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

(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(9) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(10) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?