Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3200

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

Amount (A) = $3584

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 = $3584 – $3200 = $384

Thus, Simple Interest = $384

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 × 384}/_{3200 × 4}

= ³⁸⁴⁰⁰/₁₂₈₀₀

= 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) = $3200

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

Simple Interest = $384 (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 $3200

= ⁴/₁₀₀ × 3200

= ^{4 × 3200}/₁₀₀

= ¹²⁸⁰⁰/₁₀₀ = 128

Thus, simple Interest for 1 year = $128

Now,

∵ If the simple Interest is $128, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₈ years

∴ If the simple Interest is $384, then the time = ¹/₁₂₈ × 384 years

= ^{1 × 384}/₁₂₈ years

= ³⁸⁴/₁₂₈ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.

(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.

(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.

(4) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?

(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?

(8) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?

(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.

(10) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.