Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3050

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

Amount (A) = $3324.5

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 = $3324.5 – $3050 = $274.5

Thus, Simple Interest = $274.5

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 × 274.5}/_{3050 × 3}

= ²⁷⁴⁵⁰/₉₁₅₀

= 3 years (using formula)

Thus, Time (T) = 3 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 = $274.5 (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 $274.5, then the time = ¹/_91.5 × 274.5 years

= ^{1 × 274.5}/_91.5 years

= ^274.5/_91.5 = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.

(2) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?

(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(5) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?

(6) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?

(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.

(9) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.

(10) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?