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 $10640 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $10640

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 = $10640 – $5600 = $5040

Thus, Simple Interest = $5040

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 × 5040}/_{5600 × 10}

= ⁵⁰⁴⁰⁰⁰/₅₆₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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 = $5040 (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 $5040, then the time = ¹/₅₆₀ × 5040 years

= ^{1 × 5040}/₅₆₀ years

= ⁵⁰⁴⁰/₅₆₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.

(2) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(3) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?

(4) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.

(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.

(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(9) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.

(10) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?