Question

Suppose Sydney deposits $1,000 into an account that compounds the interest twice per year at an interest rate of 5%. Every year, she deposits an additional $1,000 into the account. She does not make any withdrawals. How much money will she have in her account after 10 years? (Answers are rounded to the nearest dollar.)

A) $10,500
B) $11,730
C)$12,500
D)$14730​

Answer 1

To calculate the amount of money Sydney will have in her account after 10 years, you can use the compound interest formula. Sydney's initial deposit is $1,000 and the interest is compounded twice per year at a rate of 5%. She also makes additional deposits of $1,000 each year.

Step-by-step explanation:

To calculate the amount of money Sydney will have in her account after 10 years, we need to use the compound interest formula. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount (initial deposit), r is the interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, Sydney's initial deposit is $1,000, the interest rate is 5%, the interest is compounded twice per year, and she makes additional deposits of $1,000 each year. So, the formula becomes:

A = 1000(1 + 0.05/2)^(2*10) + 1000(1 + 0.05/2)^(2*(10-1)) + 1000(1 + 0.05/2)^(2*(10-2)) + ... + 1000(1 + 0.05/2)^(2*1) + 1000