Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (R) = 2% per annum

Amount (A) = $3294

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 = $3294 – $3050 = $244

Thus, Simple Interest = $244

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 × 244}/_{3050 × 2}

= ²⁴⁴⁰⁰/₆₁₀₀

= 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) = $3050

Rate of Simple Interest (R) = 2% per annum

Simple Interest = $244 (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 = 2% of Principal

= 2% of $3050

= ²/₁₀₀ × 3050

= ^{2 × 3050}/₁₀₀

= ⁶¹⁰⁰/₁₀₀ = 61

Thus, simple Interest for 1 year = $61

Now,

∵ If the simple Interest is $61, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₁ years

∴ If the simple Interest is $244, then the time = ¹/₆₁ × 244 years

= ^{1 × 244}/₆₁ years

= ²⁴⁴/₆₁ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.

(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(3) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

(4) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

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

(6) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(7) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.

(9) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(10) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.