Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 7% 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  8

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 7% 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 × 7}

= ²⁸⁵⁶⁰⁰/₃₅₇₀₀

= 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) = $5100

Rate of Simple Interest (R) = 7% 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 = 7% of Principal

= 7% of $5100

= ⁷/₁₀₀ × 5100

= ^{7 × 5100}/₁₀₀

= ³⁵⁷⁰⁰/₁₀₀ = 357

Thus, simple Interest for 1 year = $357

Now,

∵ If the simple Interest is $357, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₇ years

∴ If the simple Interest is $2856, then the time = ¹/₃₅₇ × 2856 years

= ^{1 × 2856}/₃₅₇ years

= ²⁸⁵⁶/₃₅₇ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) 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.

(2) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.

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

(4) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?

(6) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.

(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?

(8) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(9) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

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