Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3150

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

Amount (A) = $3622.5

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 = $3622.5 – $3150 = $472.5

Thus, Simple Interest = $472.5

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 × 472.5}/_{3150 × 3}

= ⁴⁷²⁵⁰/₉₄₅₀

= 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) = 3% per annum

Simple Interest = $472.5 (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 = 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 $472.5, then the time = ¹/_94.5 × 472.5 years

= ^{1 × 472.5}/_94.5 years

= ^472.5/_94.5 = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.

(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.

(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?

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

(7) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.

(9) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.

(10) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.