Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (R) = 2% per annum

Amount (A) = $3233

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 = $3233 – $3050 = $183

Thus, Simple Interest = $183

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 × 183}/_{3050 × 2}

= ¹⁸³⁰⁰/₆₁₀₀

= 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) = $3050

Rate of Simple Interest (R) = 2% per annum

Simple Interest = $183 (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 = 2% of Principal

= 2% of $3050

= ²/₁₀₀ × 3050

= ^{2 × 3050}/₁₀₀

= ⁶¹⁰⁰/₁₀₀ = 61

Thus, simple Interest for 1 year = $61

Now,

∵ If the simple Interest is $61, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₁ years

∴ If the simple Interest is $183, then the time = ¹/₆₁ × 183 years

= ^{1 × 183}/₆₁ years

= ¹⁸³/₆₁ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.

(3) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.

(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.

(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 6% simple interest?

(7) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?

(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.

(9) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?

(10) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.