Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3200

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

Amount (A) = $3520

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 = $3520 – $3200 = $320

Thus, Simple Interest = $320

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 × 320}/_{3200 × 2}

= ³²⁰⁰⁰/₆₄₀₀

= 5 years (using formula)

Thus, Time (T) = 5 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 = $320 (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 $320, then the time = ¹/₆₄ × 320 years

= ^{1 × 320}/₆₄ years

= ³²⁰/₆₄ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?

(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.

(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.

(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(6) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?

(7) 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.

(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 3% simple interest?

(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.

(10) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.