Question

A sum of money will be deposited today at 7 percent per year. The goal is
to have this sum grow to $105,000 in 5 years. What sum must be
deposited if interest is compounded:
i. Annually (2 marks)
ii. semiannually (2 marks)

Answer 1

Answer:

annually = 600 rupees

semi annually 300 rupees

Step-by-step explanation:

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Answer 2

Given :-

• Rate = 7% annually .
• Amount = $105,000
• Time = 5 years.

To Find :- What sum must be deposited if interest is compounded :-

• Annually .
• Semiannually .

Solution :-

Let us assume that The Principal is $ P .

Case 1 :- when rate is Annually.

→ Amount = Principal * {1 + (Rate/100)}^(time)

→ 105000 = P{1 + (7/100)}⁵

→ 105000 = P(107/100)⁵

→ P = (105000 * 100 * 100 * 100 * 100 * 100) / (107 * 107 * 107* 107 * 107)

→ P ≈ $74863.5 (Ans.)

Case 2 :- when rate is Semi - Annually .

• Rate = (7/2) = 3.5%
• Time = 5 * 2 = 10 years.

→ Amount = Principal * {1 + (Rate/100)}^(time)

→ 105000 = P{1 + (3.5/100)}¹⁰

→ 105000 = P(103.5/100)¹⁰

→ P = {105000 * (100)¹⁰} / (103.5)¹⁰

→ P ≈ $74436.5 (Ans.)

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