Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3150

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

Amount (A) = $3339

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 = $3339 – $3150 = $189

Thus, Simple Interest = $189

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 × 189}/_{3150 × 2}

= ¹⁸⁹⁰⁰/₆₃₀₀

= 3 years (using formula)

Thus, Time (T) = 3 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) = $3150

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

Simple Interest = $189 (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 $3150

= ²/₁₀₀ × 3150

= ^{2 × 3150}/₁₀₀

= ⁶³⁰⁰/₁₀₀ = 63

Thus, simple Interest for 1 year = $63

Now,

∵ If the simple Interest is $63, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₃ years

∴ If the simple Interest is $189, then the time = ¹/₆₃ × 189 years

= ^{1 × 189}/₆₃ years

= ¹⁸⁹/₆₃ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(2) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.

(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?

(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?

(5) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.

(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?

(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?

(9) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.

(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.