Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 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) = 8% per annum

Amount (A) = $8288

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 = $8288 – $5600 = $2688

Thus, Simple Interest = $2688

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 × 2688}/_{5600 × 8}

= ²⁶⁸⁸⁰⁰/₄₄₈₀₀

= 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) = 8% per annum

Simple Interest = $2688 (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 = 8% of Principal

= 8% of $5600

= ⁸/₁₀₀ × 5600

= ^{8 × 5600}/₁₀₀

= ⁴⁴⁸⁰⁰/₁₀₀ = 448

Thus, simple Interest for 1 year = $448

Now,

∵ If the simple Interest is $448, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₈ years

∴ If the simple Interest is $2688, then the time = ¹/₄₄₈ × 2688 years

= ^{1 × 2688}/₄₄₈ years

= ²⁶⁸⁸/₄₄₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.

(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?

(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?

(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(7) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?

(8) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?

(9) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?

(10) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?