Question

For her 3RD birthday, Alondra’s parents invested $14,000 in an 14- year certificate for her that pays 11% compounded every 4 months. How much is the certificate worth on Alondra’s 17th birthday

Answer 1

The certificate is worth approximately $59,320.16 on Alondra's 17th birthday.

To solve this problem

We use the compound interest formula:

`A = P * (1 + r/n)^(^n^t)`

Where:

• A is the future value of the investment
• P is the principal amount (initial investment)
• r is the annual interest rate (in decimal form)
• n is the number of times interest is compounded per year
• t is the number of years

In this case:

P = $14,000

r = 0.11 (eleven percent)

n = 4 (quarterly compounded)

t = 14 years.

Substitute these values into the formula and solve for A:

`A = 14000 * (1 + 0.0275)^(^4^ *^ 1^4^)`

`A = 14000 * 1.0275^5^6`

Now, calculate the value:

A ≈ 14000 * 4.25144

A ≈ $59,320.16

So, the certificate is worth approximately $59,320.16 on Alondra's 17th birthday.