Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3200

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

Amount (A) = $3328

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 = $3328 – $3200 = $128

Thus, Simple Interest = $128

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 × 128}/_{3200 × 2}

= ¹²⁸⁰⁰/₆₄₀₀

= 2 years (using formula)

Thus, Time (T) = 2 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) = 2% per annum

Simple Interest = $128 (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 $3200

= ²/₁₀₀ × 3200

= ^{2 × 3200}/₁₀₀

= ⁶⁴⁰⁰/₁₀₀ = 64

Thus, simple Interest for 1 year = $64

Now,

∵ If the simple Interest is $64, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₄ years

∴ If the simple Interest is $128, then the time = ¹/₆₄ × 128 years

= ^{1 × 128}/₆₄ years

= ¹²⁸/₆₄ = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.

(3) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

(4) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.

(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 4% simple interest?

(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?

(8) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.

(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.