Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3200

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

Amount (A) = $3680

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 = $3680 – $3200 = $480

Thus, Simple Interest = $480

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 × 480}/_{3200 × 3}

= ⁴⁸⁰⁰⁰/₉₆₀₀

= 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) = $3200

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

Simple Interest = $480 (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 $3200

= ³/₁₀₀ × 3200

= ^{3 × 3200}/₁₀₀

= ⁹⁶⁰⁰/₁₀₀ = 96

Thus, simple Interest for 1 year = $96

Now,

∵ If the simple Interest is $96, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₆ years

∴ If the simple Interest is $480, then the time = ¹/₉₆ × 480 years

= ^{1 × 480}/₉₆ years

= ⁴⁸⁰/₉₆ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

(4) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.

(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.

(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?

(8) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?

(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.

(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.