Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3000

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

Amount (A) = $3750

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 = $3750 – $3000 = $750

Thus, Simple Interest = $750

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 × 750}/_{3000 × 5}

= ⁷⁵⁰⁰⁰/₁₅₀₀₀

= 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) = $3000

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

Simple Interest = $750 (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 $3000

= ⁵/₁₀₀ × 3000

= ^{5 × 3000}/₁₀₀

= ¹⁵⁰⁰⁰/₁₀₀ = 150

Thus, simple Interest for 1 year = $150

Now,

∵ If the simple Interest is $150, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₅₀ years

∴ If the simple Interest is $750, then the time = ¹/₁₅₀ × 750 years

= ^{1 × 750}/₁₅₀ years

= ⁷⁵⁰/₁₅₀ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.

(2) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.

(3) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?

(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

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

(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?

(8) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

(9) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.

(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 5% simple interest?