Question

Ezra opened a savings account and deposited $1,542.00. The account earns 10% interest,compounded quarterly. If he wants to use the money to buy a new bicycle in 3 years, howmuch will he be able to spend on the bike?ntUse the formula A = P(1 + )".A P1 where A is the balance (final amount), P is the principal(starting amount), r is the interest rate expressed as a decimal, n is the number of times peryear that the interest is compounded, and t is the time in years.Round your answer to the nearest cent

Answer 1

Given:

• Principal, P = $1,542.00

,

• Interest rate, r = 10% = 0.10

,

• Number of times compounded, n = quarterly = 4 times a year

,

• Time, t = 3 years.

Let's find the amount he will have after 3 years to spend on the bike.

Apply the compound interest formula:

$A=P(1+\frac{r}{n})^{nt}$

Where:

P = 1542

r = 0.10

n = 4

t = 3

Plug in the values and solve for the final amount A:

$\begin{gathered} A=1542(1+\frac{0.10}{4})^{4*3} \\ \\ A=1542(1+0.025)^{12} \\ \\ A=1542(1.025)^{12} \\ \\ A=1542(1.344888824) \\ \\ A=2073.82 \end{gathered}$

Therefore, he will have $2073.82 to spend on the bike.

ANSWER:

$2,073.82