Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (R) = 3% per annum

Amount (A) = $3528

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 = $3528 – $3150 = $378

Thus, Simple Interest = $378

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 × 378}/_{3150 × 3}

= ³⁷⁸⁰⁰/₉₄₅₀

= 4 years (using formula)

Thus, Time (T) = 4 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) = 3% per annum

Simple Interest = $378 (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 $3150

= ³/₁₀₀ × 3150

= ^{3 × 3150}/₁₀₀

= ⁹⁴⁵⁰/₁₀₀ = 94.5

Thus, simple Interest for 1 year = $94.5

Now,

∵ If the simple Interest is $94.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_94.5 years

∴ If the simple Interest is $378, then the time = ¹/_94.5 × 378 years

= ^{1 × 378}/_94.5 years

= ³⁷⁸/_94.5 = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.

(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

(3) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.

(4) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.

(5) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(6) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 3 years.

(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.

(9) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?