Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3200

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

Amount (A) = $3392

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 = $3392 – $3200 = $192

Thus, Simple Interest = $192

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 × 192}/_{3200 × 3}

= ¹⁹²⁰⁰/₉₆₀₀

= 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) = 3% per annum

Simple Interest = $192 (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 $192, then the time = ¹/₉₆ × 192 years

= ^{1 × 192}/₉₆ years

= ¹⁹²/₉₆ = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.

(3) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.

(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?

(5) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

(8) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?

(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.