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 $8960 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $8960

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 = $8960 – $5600 = $3360

Thus, Simple Interest = $3360

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 × 3360}/_{5600 × 10}

= ³³⁶⁰⁰⁰/₅₆₀₀₀

= 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) = $5600

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

Simple Interest = $3360 (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 $3360, then the time = ¹/₅₆₀ × 3360 years

= ^{1 × 3360}/₅₆₀ years

= ³³⁶⁰/₅₆₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(2) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

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

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.

(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 5% simple interest?

(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?

(7) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?

(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?

(9) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.