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) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(3) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?

(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(5) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.

(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 4 years.

(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(9) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.

(10) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?