Question

At the time of her​ grandson's birth, a grandmother deposits $ 11000 in an account that pays 2.5 % 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? The value of the account will be ​$= ​(Round to the nearest dollar as​ needed.)

Answer 1

To solve this problem, we can use the formula for compound interest:

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

where:

A = final amount

P = principal (initial amount)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = time (in years)

In this case:

P = $11,000

r = 2.5% = 0.025 (since it's compounded monthly, we need to divide by 12 to get the monthly rate)

n = 12 (compounded monthly)

t = 21 years

Plugging in these values, we get:

A = 11000(1 + 0.025/12)^(12*21)

A ≈ $16,180.64

Therefore, the value of the account at the child's twenty-first birthday will be approximately $16,181.