Simple Interest
Math MCQs

Question :    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.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5400

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $7992

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 = $7992 – $5400 = $2592

Thus, Simple Interest = $2592

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 × 2592}/_{5400 × 8}

= ²⁵⁹²⁰⁰/₄₃₂₀₀

= 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) = $5400

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2592 (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 = 8% of Principal

= 8% of $5400

= ⁸/₁₀₀ × 5400

= ^{8 × 5400}/₁₀₀

= ⁴³²⁰⁰/₁₀₀ = 432

Thus, simple Interest for 1 year = $432

Now,

∵ If the simple Interest is $432, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₂ years

∴ If the simple Interest is $2592, then the time = ¹/₄₃₂ × 2592 years

= ^{1 × 2592}/₄₃₂ years

= ²⁵⁹²/₄₃₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?

(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(3) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.

(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?

(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.

(7) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?

(8) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?