Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $10492

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 = $10492 – $6100 = $4392

Thus, Simple Interest = $4392

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 × 4392}/_{6100 × 9}

= ⁴³⁹²⁰⁰/₅₄₉₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $6100

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

Simple Interest = $4392 (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 $6100

= ⁹/₁₀₀ × 6100

= ^{9 × 6100}/₁₀₀

= ⁵⁴⁹⁰⁰/₁₀₀ = 549

Thus, simple Interest for 1 year = $549

Now,

∵ If the simple Interest is $549, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₉ years

∴ If the simple Interest is $4392, then the time = ¹/₅₄₉ × 4392 years

= ^{1 × 4392}/₅₄₉ years

= ⁴³⁹²/₅₄₉ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.

(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.

(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?

(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.

(7) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.

(8) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?

(10) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?