Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6900

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $13800

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 = $13800 – $6900 = $6900

Thus, Simple Interest = $6900

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 × 6900}/_{6900 × 10}

= ⁶⁹⁰⁰⁰⁰/₆₉₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $6900

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $6900 (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 = 10% of Principal

= 10% of $6900

= ¹⁰/₁₀₀ × 6900

= ^{10 × 6900}/₁₀₀

= ⁶⁹⁰⁰⁰/₁₀₀ = 690

Thus, simple Interest for 1 year = $690

Now,

∵ If the simple Interest is $690, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₉₀ years

∴ If the simple Interest is $6900, then the time = ¹/₆₉₀ × 6900 years

= ^{1 × 6900}/₆₉₀ years

= ⁶⁹⁰⁰/₆₉₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.

(2) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.

(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?

(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?

(6) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?

(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?

(8) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?

(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(10) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.