Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3200

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $4000

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 = $4000 – $3200 = $800

Thus, Simple Interest = $800

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 × 800}/_{3200 × 5}

= ⁸⁰⁰⁰⁰/₁₆₀₀₀

= 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) = $3200

Rate of Simple Interest (R) = 5% per annum

Simple Interest = $800 (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 = 5% of Principal

= 5% of $3200

= ⁵/₁₀₀ × 3200

= ^{5 × 3200}/₁₀₀

= ¹⁶⁰⁰⁰/₁₀₀ = 160

Thus, simple Interest for 1 year = $160

Now,

∵ If the simple Interest is $160, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₆₀ years

∴ If the simple Interest is $800, then the time = ¹/₁₆₀ × 800 years

= ^{1 × 800}/₁₆₀ years

= ⁸⁰⁰/₁₆₀ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(2) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(4) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(5) How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?

(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

(7) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.

(10) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?