Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $9520

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 = $9520 – $5600 = $3920

Thus, Simple Interest = $3920

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 × 3920}/_{5600 × 10}

= ³⁹²⁰⁰⁰/₅₆₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $5600

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

Simple Interest = $3920 (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 $5600

= ¹⁰/₁₀₀ × 5600

= ^{10 × 5600}/₁₀₀

= ⁵⁶⁰⁰⁰/₁₀₀ = 560

Thus, simple Interest for 1 year = $560

Now,

∵ If the simple Interest is $560, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₆₀ years

∴ If the simple Interest is $3920, then the time = ¹/₅₆₀ × 3920 years

= ^{1 × 3920}/₅₆₀ years

= ³⁹²⁰/₅₆₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?

(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.

(6) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

(7) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?

(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.

(9) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.