Question

what amount must be acoposited by a 15 years old student in a bank that pays 1% compounded anually so that after 10 years he will have 20,000

Answer 1

Explanation:

To calculate the initial deposit required, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = future value of the investment (20,000)

P = principal amount (initial deposit)

r = annual interest rate (1% or 0.01)

n = number of times interest is compounded per year (1, as it's compounded annually)

t = number of years (10)

Plugging in the values, we get:

20,000 = P(1 + 0.01/1)^(1*10)

Simplifying:

20,000 = P(1.01)^10

Next, divide both sides of the equation by (1.01)^10 to isolate P:

P = 20,000 / (1.01)^10

Using a calculator, we find:

P ≈ 18,303.58

Therefore, the 15-year-old student must deposit approximately $18,303.58 in the bank.