Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (R) = 4% 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 × 4}

= ²⁵²⁰⁰/₁₂₆₀₀

= 2 years (using formula)

Thus, Time (T) = 2 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 = $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 = 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 $252, then the time = ¹/₁₂₆ × 252 years

= ^{1 × 252}/₁₂₆ years

= ²⁵²/₁₂₆ = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?

(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.

(5) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?

(6) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?

(8) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(9) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.