Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5900

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

Amount (A) = $9204

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 = $9204 – $5900 = $3304

Thus, Simple Interest = $3304

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 × 3304}/_{5900 × 8}

= ³³⁰⁴⁰⁰/₄₇₂₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $5900

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

Simple Interest = $3304 (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 $5900

= ⁸/₁₀₀ × 5900

= ^{8 × 5900}/₁₀₀

= ⁴⁷²⁰⁰/₁₀₀ = 472

Thus, simple Interest for 1 year = $472

Now,

∵ If the simple Interest is $472, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₂ years

∴ If the simple Interest is $3304, then the time = ¹/₄₇₂ × 3304 years

= ^{1 × 3304}/₄₇₂ years

= ³³⁰⁴/₄₇₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.

(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

(3) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.

(4) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

(5) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.

(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?

(10) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?