Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3200

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

Amount (A) = $3488

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 = $3488 – $3200 = $288

Thus, Simple Interest = $288

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 × 288}/_{3200 × 3}

= ²⁸⁸⁰⁰/₉₆₀₀

= 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) = 3% per annum

Simple Interest = $288 (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 $3200

= ³/₁₀₀ × 3200

= ^{3 × 3200}/₁₀₀

= ⁹⁶⁰⁰/₁₀₀ = 96

Thus, simple Interest for 1 year = $96

Now,

∵ If the simple Interest is $96, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₆ years

∴ If the simple Interest is $288, then the time = ¹/₉₆ × 288 years

= ^{1 × 288}/₉₆ years

= ²⁸⁸/₉₆ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.

(3) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.

(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?

(6) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?

(8) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.

(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?

(10) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.