Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 7% 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  8

Solution & Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (R) = 7% 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 × 7}

= ³³⁰⁴⁰⁰/₄₁₃₀₀

= 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) = $5900

Rate of Simple Interest (R) = 7% 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 = 7% of Principal

= 7% of $5900

= ⁷/₁₀₀ × 5900

= ^{7 × 5900}/₁₀₀

= ⁴¹³⁰⁰/₁₀₀ = 413

Thus, simple Interest for 1 year = $413

Now,

∵ If the simple Interest is $413, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₃ years

∴ If the simple Interest is $3304, then the time = ¹/₄₁₃ × 3304 years

= ^{1 × 3304}/₄₁₃ years

= ³³⁰⁴/₄₁₃ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.

(3) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.

(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.

(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?

(7) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(8) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.

(9) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?

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