Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3100

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

Amount (A) = $3720

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 = $3720 – $3100 = $620

Thus, Simple Interest = $620

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 × 620}/_{3100 × 4}

= ⁶²⁰⁰⁰/₁₂₄₀₀

= 5 years (using formula)

Thus, Time (T) = 5 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) = $3100

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

Simple Interest = $620 (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 $3100

= ⁴/₁₀₀ × 3100

= ^{4 × 3100}/₁₀₀

= ¹²⁴⁰⁰/₁₀₀ = 124

Thus, simple Interest for 1 year = $124

Now,

∵ If the simple Interest is $124, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₄ years

∴ If the simple Interest is $620, then the time = ¹/₁₂₄ × 620 years

= ^{1 × 620}/₁₂₄ years

= ⁶²⁰/₁₂₄ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?

(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.

(4) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?

(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?

(7) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

(8) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.

(9) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?