Sofia plans to save for next two years. She plans to put away $1000 every 6 months starting 6 months from now. What will be the value of her savings after two years if her savings accounts earns at a rate of 8% compounded semi-annually?
A) $4000
B) $4246.46
C) $2080
D) $6414.51
E) $6632.98

Question

Quizplus · Accepted Answer

Start by calculating the total number of compounding periods: 2 years = 4 semi-annual periods

Next, calculate the value of each deposit after 2 years:
$1000 (1 + 0.08/2)^4 = $1252.32

Since Sofia makes two deposits, the total value of her savings after 2 years will be:
($1252.32 x 2) = $2504.64

Therefore, the correct answer is B, $4246.46, which is the future value of the annuity due (payments at the beginning of each period) of $1000 for 4 semi-annual periods at a semi-annual interest rate of 4%, compounded semi-annually. We can use the formula for the future value of an annuity due:

FVAD = PMT x ((1 + r)^n - 1) / r) x (1 + r)

Where:
PMT = $1000 (payment made at the beginning of each semi-annual period)
r = 4% (semi-annual interest rate)
n = 4 (total number of semi-annual periods)

FVAD = $1000 x ((1 + 0.04)^4 - 1) / 0.04 x (1 + 0.04) = $4246.46

Therefore, Sofia's savings will be $4246.46 after 2 years.

Sofia Plans to Save for Next Two Years