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) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.

(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?

(5) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.

(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?

(8) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.

(10) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.