Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (R) = 2% per annum

Amount (A) = $3465

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 = $3465 – $3150 = $315

Thus, Simple Interest = $315

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 × 315}/_{3150 × 2}

= ³¹⁵⁰⁰/₆₃₀₀

= 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) = $3150

Rate of Simple Interest (R) = 2% per annum

Simple Interest = $315 (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 = 2% of Principal

= 2% of $3150

= ²/₁₀₀ × 3150

= ^{2 × 3150}/₁₀₀

= ⁶³⁰⁰/₁₀₀ = 63

Thus, simple Interest for 1 year = $63

Now,

∵ If the simple Interest is $63, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₃ years

∴ If the simple Interest is $315, then the time = ¹/₆₃ × 315 years

= ^{1 × 315}/₆₃ years

= ³¹⁵/₆₃ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.

(2) How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?

(3) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(4) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?

(5) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(8) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.

(9) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.

(10) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?