Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3937.5

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 = $3937.5 – $3150 = $787.5

Thus, Simple Interest = $787.5

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 × 787.5}/_{3150 × 5}

= ⁷⁸⁷⁵⁰/₁₅₇₅₀

= 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) = $3150

Rate of Simple Interest (R) = 5% per annum

Simple Interest = $787.5 (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 = 5% of Principal

= 5% of $3150

= ⁵/₁₀₀ × 3150

= ^{5 × 3150}/₁₀₀

= ¹⁵⁷⁵⁰/₁₀₀ = 157.5

Thus, simple Interest for 1 year = $157.5

Now,

∵ If the simple Interest is $157.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_157.5 years

∴ If the simple Interest is $787.5, then the time = ¹/_157.5 × 787.5 years

= ^{1 × 787.5}/_157.5 years

= ^787.5/_157.5 = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.

(3) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?

(5) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 7 years.

(7) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.

(9) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(10) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.