Simple Interest
Math MCQs

Question :    David took a loan of $4800 at the rate of 10% 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  6

Solution & Explanation

Solution

Given,

Principal (P) = $4800

Rate of Simple Interest (R) = 10% 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 × 10}

= ²⁸⁸⁰⁰⁰/₄₈₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = 10% 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 = 10% of Principal

= 10% of $4800

= ¹⁰/₁₀₀ × 4800

= ^{10 × 4800}/₁₀₀

= ⁴⁸⁰⁰⁰/₁₀₀ = 480

Thus, simple Interest for 1 year = $480

Now,

∵ If the simple Interest is $480, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₀ years

∴ If the simple Interest is $2880, then the time = ¹/₄₈₀ × 2880 years

= ^{1 × 2880}/₄₈₀ years

= ²⁸⁸⁰/₄₈₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.

(4) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.

(5) 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.

(6) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.

(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(9) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.