Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (R) = 4% per annum

Amount (A) = $3780

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 = $3780 – $3150 = $630

Thus, Simple Interest = $630

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 × 630}/_{3150 × 4}

= ⁶³⁰⁰⁰/₁₂₆₀₀

= 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) = 4% per annum

Simple Interest = $630 (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 = 4% of Principal

= 4% of $3150

= ⁴/₁₀₀ × 3150

= ^{4 × 3150}/₁₀₀

= ¹²⁶⁰⁰/₁₀₀ = 126

Thus, simple Interest for 1 year = $126

Now,

∵ If the simple Interest is $126, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₆ years

∴ If the simple Interest is $630, then the time = ¹/₁₂₆ × 630 years

= ^{1 × 630}/₁₂₆ years

= ⁶³⁰/₁₂₆ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(2) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.

(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?

(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.

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

(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(8) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.