Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3150

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

Amount (A) = $3528

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 = $3528 – $3150 = $378

Thus, Simple Interest = $378

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 × 378}/_{3150 × 4}

= ³⁷⁸⁰⁰/₁₂₆₀₀

= 3 years (using formula)

Thus, Time (T) = 3 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 = $378 (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 $378, then the time = ¹/₁₂₆ × 378 years

= ^{1 × 378}/₁₂₆ years

= ³⁷⁸/₁₂₆ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?

(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?

(3) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?

(4) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.

(6) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 3 years.

(7) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?

(8) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.

(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.

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