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 $8378 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $8378

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 = $8378 – $5900 = $2478

Thus, Simple Interest = $2478

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 × 2478}/_{5900 × 7}

= ²⁴⁷⁸⁰⁰/₄₁₃₀₀

= 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) = $5900

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2478 (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 $2478, then the time = ¹/₄₁₃ × 2478 years

= ^{1 × 2478}/₄₁₃ years

= ²⁴⁷⁸/₄₁₃ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.

(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?

(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.

(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.

(5) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

(6) 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.

(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(8) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.

(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?

(10) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.