Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $7956

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 = $7956 – $5100 = $2856

Thus, Simple Interest = $2856

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 × 2856}/_{5100 × 8}

= ²⁸⁵⁶⁰⁰/₄₀₈₀₀

= 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) = $5100

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2856 (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 $5100

= ⁸/₁₀₀ × 5100

= ^{8 × 5100}/₁₀₀

= ⁴⁰⁸⁰⁰/₁₀₀ = 408

Thus, simple Interest for 1 year = $408

Now,

∵ If the simple Interest is $408, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₈ years

∴ If the simple Interest is $2856, then the time = ¹/₄₀₈ × 2856 years

= ^{1 × 2856}/₄₀₈ years

= ²⁸⁵⁶/₄₀₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(2) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.

(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(6) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.

(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(8) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

(9) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?

(10) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?