Question

A deposit of $90 is placed into a college fund at the beginning of every week for 5 years. The fund earns 3% annual interest, compounded weekly, and paid at the end of the week. How much is in the account right after the last deposit

Answer 1

Step-by-step explanation:

The value of the initial deposit is $90, so a1=90. A total of 260 weekly deposits are made in the 5 years, so n=260. To find r, divide the annual interest rate by 52 to find the weekly interest rate and add 1 to represent the new weekly deposit.

r=1+0.0352=1.00057692308

Substitute a1=90, n=260, and r=1.00057692308 into the formula for the sum of the first n terms of a geometric series and simplify to find the value of the annuity.

S260= 90(1−1.00057692308260) / 1−1.00057692308 ≈25238.31

Therefore, to the nearest dollar, the account has $25,238 after the last deposit is made.

This is the correct answer for Knewton. That's the explanation.

Answer 2

$25,249.50

Step-by-step explanation:

Deposit at the beginning of every 6 month (A) = 90

Time period (t) = 5

n = 52

Rate (r) = 3% = 0.03

So, the net amount in the account right after the last deposit is as follows:

= A * [(1+r/n)^(n*t) - 1 / r/n] * (1 + r/n)

= 90 * [(1+0.03/52)^(52*5) - 1 / 0.03/52] * (1 + 0.03/52)

= 90 * [(1.16178399147 - 1 / 0.000577] * (1+0.000577)

= 90 * 280.3882 * 1.000577

= 25249.498559226

= $25,249.50