Question

Elaine received $20000 as a gift on New Year's Day (January 1) in the past, and she put the money into a bank account that same day. It is now New Year's Day less than a decade later, and she has $36769.18 in the account. This bank account pays 7% per year, and she has not added or taken out money since the initial deposit. How many years ago did she receive this gift? Give your answer as an integer (the number of years). Elaine received this gift

Answer 1

To find out how many years ago Elaine received the gift, we can use the compound interest formula: A = P(1 + r/n)^(nt). Plugging in the values, we find that Elaine received the gift nearly 9 years ago.

Step-by-step explanation:

To find out how many years ago Elaine received the gift, we can use the compound interest formula:

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

Where:

• A is the final amount in the account ($36,769.18)
• P is the initial deposit ($20,000)
• r is the annual interest rate (7% or 0.07 as a decimal)
• n is the number of times the interest is compounded per year (assume it is compounded once per year)
• t is the number of years

Plugging in the values, we have:

$36,769.18 = $20,000(1 + 0.07/1)^(1t)

Simplifying the equation, we get:

1.8384595 = (1.07)^t

Using logarithms, we can solve for t:

t = log(1.8384595)/log(1.07)

t ≈ 9.3

Therefore, Elaine received the gift nearly 9 years ago.