Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 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) = 7% per annum

Amount (A) = $9128

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 = $9128 – $5600 = $3528

Thus, Simple Interest = $3528

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 × 3528}/_{5600 × 7}

= ³⁵²⁸⁰⁰/₃₉₂₀₀

= 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) = 7% per annum

Simple Interest = $3528 (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 = 7% of Principal

= 7% of $5600

= ⁷/₁₀₀ × 5600

= ^{7 × 5600}/₁₀₀

= ³⁹²⁰⁰/₁₀₀ = 392

Thus, simple Interest for 1 year = $392

Now,

∵ If the simple Interest is $392, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₂ years

∴ If the simple Interest is $3528, then the time = ¹/₃₉₂ × 3528 years

= ^{1 × 3528}/₃₉₂ years

= ³⁵²⁸/₃₉₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?

(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(5) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?

(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.

(9) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(10) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.