Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (R) = 3% per annum

Amount (A) = $3507.5

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 = $3507.5 – $3050 = $457.5

Thus, Simple Interest = $457.5

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 × 457.5}/_{3050 × 3}

= ⁴⁵⁷⁵⁰/₉₁₅₀

= 5 years (using formula)

Thus, Time (T) = 5 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) = 3% per annum

Simple Interest = $457.5 (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 = 3% of Principal

= 3% of $3050

= ³/₁₀₀ × 3050

= ^{3 × 3050}/₁₀₀

= ⁹¹⁵⁰/₁₀₀ = 91.5

Thus, simple Interest for 1 year = $91.5

Now,

∵ If the simple Interest is $91.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_91.5 years

∴ If the simple Interest is $457.5, then the time = ¹/_91.5 × 457.5 years

= ^{1 × 457.5}/_91.5 years

= ^457.5/_91.5 = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.

(2) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.

(3) 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.

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.

(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(6) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.

(7) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(9) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.