Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3000

Rate of Simple Interest (R) = 3% per annum

Amount (A) = $3360

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 = $3360 – $3000 = $360

Thus, Simple Interest = $360

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 × 360}/_{3000 × 3}

= ³⁶⁰⁰⁰/₉₀₀₀

= 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) = $3000

Rate of Simple Interest (R) = 3% per annum

Simple Interest = $360 (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 = 3% of Principal

= 3% of $3000

= ³/₁₀₀ × 3000

= ^{3 × 3000}/₁₀₀

= ⁹⁰⁰⁰/₁₀₀ = 90

Thus, simple Interest for 1 year = $90

Now,

∵ If the simple Interest is $90, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₀ years

∴ If the simple Interest is $360, then the time = ¹/₉₀ × 360 years

= ^{1 × 360}/₉₀ years

= ³⁶⁰/₉₀ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

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

(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(3) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?

(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 5% simple interest?

(5) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

(7) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(9) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?

(10) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?