Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4100

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $6314

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 = $6314 – $4100 = $2214

Thus, Simple Interest = $2214

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 × 2214}/_{4100 × 9}

= ²²¹⁴⁰⁰/₃₆₉₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $4100

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $2214 (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 = 9% of Principal

= 9% of $4100

= ⁹/₁₀₀ × 4100

= ^{9 × 4100}/₁₀₀

= ³⁶⁹⁰⁰/₁₀₀ = 369

Thus, simple Interest for 1 year = $369

Now,

∵ If the simple Interest is $369, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₉ years

∴ If the simple Interest is $2214, then the time = ¹/₃₆₉ × 2214 years

= ^{1 × 2214}/₃₆₉ years

= ²²¹⁴/₃₆₉ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.

(2) If John borrowed $3200 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?

(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.

(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?

(8) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.

(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.