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 $7680 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4800

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

Amount (A) = $7680

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 = $7680 – $4800 = $2880

Thus, Simple Interest = $2880

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 × 2880}/_{4800 × 6}

= ²⁸⁸⁰⁰⁰/₂₈₈₀₀

= 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) = $4800

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

Simple Interest = $2880 (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 $2880, then the time = ¹/₂₈₈ × 2880 years

= ^{1 × 2880}/₂₈₈ years

= ²⁸⁸⁰/₂₈₈ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?

(2) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?

(3) 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.

(4) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.

(5) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(6) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?

(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(8) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(9) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.