Answer:
$25,249.50
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
Answer:
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.
