Question

At the time of her​ grandson's birth, a grandmother deposits 9,000 in an account that pays 3% compounded monthly. What will be the value of the account at the​ child's twenty-first​ birthday, assuming that no other deposits or withdrawals are made during this​ period?

Answer 1

To find out the account's value on the child's twenty-first birthday, we apply the compound interest formula with the provided information, yielding an approximate future value of $18,273.45.

Step-by-step explanation:

To determine the value of the account on the grandson's twenty-first birthday, we use the formula for compound interest

Future Value (FV) = P(1 + r/n)^(nt)

Where:

• P = principal amount (initial deposit)
• r = annual interest rate (decimal)
• n = number of times the interest is compounded per year
• t = number of years

Given the data:

• P = $9,000
• r = 3% or 0.03
• n = 12 (since the interest is compounded monthly)
• t = 21 years

Now, plugging in the values:

FV = 9000 * (1 + 0.03/12)^(12*21)

Calculating the power and multiplication gives us:

FV = 9000 * (1 + 0.0025)^(252)

FV ≈ 9000 * (1.0025)^252

FV ≈ 9000 * 2.030383777

FV ≈ $18,273.45 (rounded to two decimal places)

The account will be worth approximately $18,273.45 on the child's twenty-first birthday.