Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3780

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 = $3780 – $3150 = $630

Thus, Simple Interest = $630

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 × 630}/_{3150 × 5}

= ⁶³⁰⁰⁰/₁₅₇₅₀

= 4 years (using formula)

Thus, Time (T) = 4 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) = $3150

Rate of Simple Interest (R) = 5% per annum

Simple Interest = $630 (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 = 5% of Principal

= 5% of $3150

= ⁵/₁₀₀ × 3150

= ^{5 × 3150}/₁₀₀

= ¹⁵⁷⁵⁰/₁₀₀ = 157.5

Thus, simple Interest for 1 year = $157.5

Now,

∵ If the simple Interest is $157.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_157.5 years

∴ If the simple Interest is $630, then the time = ¹/_157.5 × 630 years

= ^{1 × 630}/_157.5 years

= ⁶³⁰/_157.5 = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(3) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(4) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

(5) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?

(6) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.

(7) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(9) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?