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 Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.

(2) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

(3) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(4) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.

(5) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?

(6) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.

(8) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.

(9) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.