Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3150

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

Amount (A) = $3402

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 = $3402 – $3150 = $252

Thus, Simple Interest = $252

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 × 252}/_{3150 × 2}

= ²⁵²⁰⁰/₆₃₀₀

= 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) = 2% per annum

Simple Interest = $252 (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 $252, then the time = ¹/₆₃ × 252 years

= ^{1 × 252}/₆₃ years

= ²⁵²/₆₃ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.

(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?

(4) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(7) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.

(9) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(10) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.