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) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.

(3) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?

(4) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.

(7) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?

(10) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.