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 $8856 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5400

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

Amount (A) = $8856

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 = $8856 – $5400 = $3456

Thus, Simple Interest = $3456

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 × 3456}/_{5400 × 8}

= ³⁴⁵⁶⁰⁰/₄₃₂₀₀

= 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) = $5400

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

Simple Interest = $3456 (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 $3456, then the time = ¹/₄₃₂ × 3456 years

= ^{1 × 3456}/₄₃₂ years

= ³⁴⁵⁶/₄₃₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.

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

(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.

(6) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.

(7) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?

(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?

(10) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?