Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4000

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $6800

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 = $6800 – $4000 = $2800

Thus, Simple Interest = $2800

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 × 2800}/_{4000 × 7}

= ²⁸⁰⁰⁰⁰/₂₈₀₀₀

= 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) = $4000

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2800 (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 = 7% of Principal

= 7% of $4000

= ⁷/₁₀₀ × 4000

= ^{7 × 4000}/₁₀₀

= ²⁸⁰⁰⁰/₁₀₀ = 280

Thus, simple Interest for 1 year = $280

Now,

∵ If the simple Interest is $280, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₀ years

∴ If the simple Interest is $2800, then the time = ¹/₂₈₀ × 2800 years

= ^{1 × 2800}/₂₈₀ years

= ²⁸⁰⁰/₂₈₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.

(2) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?

(3) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?

(4) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.

(6) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

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

(8) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?

(10) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?