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 Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?

(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?

(3) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.

(5) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.

(8) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.