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 after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.

(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?

(3) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.

(4) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.

(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.

(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?

(7) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.

(8) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?

(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?

(10) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.