Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (R) = 4% per annum

Amount (A) = $3294

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 = $3294 – $3050 = $244

Thus, Simple Interest = $244

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 × 244}/_{3050 × 4}

= ²⁴⁴⁰⁰/₁₂₂₀₀

= 2 years (using formula)

Thus, Time (T) = 2 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) = $3050

Rate of Simple Interest (R) = 4% per annum

Simple Interest = $244 (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 = 4% of Principal

= 4% of $3050

= ⁴/₁₀₀ × 3050

= ^{4 × 3050}/₁₀₀

= ¹²²⁰⁰/₁₀₀ = 122

Thus, simple Interest for 1 year = $122

Now,

∵ If the simple Interest is $122, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₂ years

∴ If the simple Interest is $244, then the time = ¹/₁₂₂ × 244 years

= ^{1 × 244}/₁₂₂ years

= ²⁴⁴/₁₂₂ = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?

(2) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?

(3) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.

(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.

(6) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?

(8) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.

(10) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?