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 $8236 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) = 7% per annum

Amount (A) = $8236

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 = $8236 – $5800 = $2436

Thus, Simple Interest = $2436

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 × 2436}/_{5800 × 7}

= ²⁴³⁶⁰⁰/₄₀₆₀₀

= 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) = 7% per annum

Simple Interest = $2436 (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 $2436, then the time = ¹/₄₀₆ × 2436 years

= ^{1 × 2436}/₄₀₆ years

= ²⁴³⁶/₄₀₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?

(2) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.

(3) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?

(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?

(6) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(9) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?