Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3000

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

= ³⁶⁰⁰⁰/₁₂₀₀₀

= 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) = $3000

Rate of Simple Interest (R) = 4% 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 = 4% of Principal

= 4% of $3000

= ⁴/₁₀₀ × 3000

= ^{4 × 3000}/₁₀₀

= ¹²⁰⁰⁰/₁₀₀ = 120

Thus, simple Interest for 1 year = $120

Now,

∵ If the simple Interest is $120, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₀ years

∴ If the simple Interest is $360, then the time = ¹/₁₂₀ × 360 years

= ^{1 × 360}/₁₂₀ years

= ³⁶⁰/₁₂₀ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 7 years.

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.

(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?

(5) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?

(7) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.

(9) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.