Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5800

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $9048

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 = $9048 – $5800 = $3248

Thus, Simple Interest = $3248

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 × 3248}/_{5800 × 7}

= ³²⁴⁸⁰⁰/₄₀₆₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 7% per annum

Simple Interest = $3248 (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 $5800

= ⁷/₁₀₀ × 5800

= ^{7 × 5800}/₁₀₀

= ⁴⁰⁶⁰⁰/₁₀₀ = 406

Thus, simple Interest for 1 year = $406

Now,

∵ If the simple Interest is $406, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₆ years

∴ If the simple Interest is $3248, then the time = ¹/₄₀₆ × 3248 years

= ^{1 × 3248}/₄₀₆ years

= ³²⁴⁸/₄₀₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.

(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.

(3) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?

(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.

(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.