Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5800

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7888

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 = $7888 – $5800 = $2088

Thus, Simple Interest = $2088

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 × 2088}/_{5800 × 6}

= ²⁰⁸⁸⁰⁰/₃₄₈₀₀

= 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) = $5800

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2088 (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 = 6% of Principal

= 6% of $5800

= ⁶/₁₀₀ × 5800

= ^{6 × 5800}/₁₀₀

= ³⁴⁸⁰⁰/₁₀₀ = 348

Thus, simple Interest for 1 year = $348

Now,

∵ If the simple Interest is $348, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₈ years

∴ If the simple Interest is $2088, then the time = ¹/₃₄₈ × 2088 years

= ^{1 × 2088}/₃₄₈ years

= ²⁰⁸⁸/₃₄₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.

(5) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.

(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?

(8) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(9) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.