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) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(2) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(3) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.

(5) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?

(6) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.

(7) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(8) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.

(10) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?