Simple Interest
Math MCQs

Question :  ( 1 of 10 )  In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3050

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

Amount (A) = $3355

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 = $3355 – $3050 = $305

Thus, Simple Interest = $305

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 × 305}/_{3050 × 2}

= ³⁰⁵⁰⁰/₆₁₀₀

= 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) = $3050

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

Simple Interest = $305 (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 $305, then the time = ¹/₆₁ × 305 years

= ^{1 × 305}/₆₁ years

= ³⁰⁵/₆₁ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.

(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?

(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?

(5) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.

(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) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.

(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?

(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?