Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (R) = 4% per annum

Amount (A) = $3654

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 = $3654 – $3150 = $504

Thus, Simple Interest = $504

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 × 504}/_{3150 × 4}

= ⁵⁰⁴⁰⁰/₁₂₆₀₀

= 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) = 4% per annum

Simple Interest = $504 (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 = 4% of Principal

= 4% of $3150

= ⁴/₁₀₀ × 3150

= ^{4 × 3150}/₁₀₀

= ¹²⁶⁰⁰/₁₀₀ = 126

Thus, simple Interest for 1 year = $126

Now,

∵ If the simple Interest is $126, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₆ years

∴ If the simple Interest is $504, then the time = ¹/₁₂₆ × 504 years

= ^{1 × 504}/₁₂₆ years

= ⁵⁰⁴/₁₂₆ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(2) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.

(6) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.

(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.

(9) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(10) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.