"Find the savings plan balance after 12 months..." solved and explained

High School
Algebra
Pre-Algebra
Ratios, rates, proportions

ediculeN

Answered question

2021-06-05

Find the savings plan balance after 12 months with an APR of 30% and monthly payments of 75$.

Answer & Explanation

l1koV

Skilled2021-06-06Added 100 answers

The formula for this calculation in Future $V a l u e = P a y m e n t [\frac{(1 + I) n - 1}{I}]$ , where $I = i n t e r e s t$ rate, and $n = p e r i o d s$ .
In this case, $P = $ 75 / m o n t h, n = 12 m o n t h s, a n d I = 30$ per year.
Since the information involves months instead of years it is necessary to divide the interest rate by 12 to obtain the monthly rate. So, $0, 3 / 12 = 0.025$
We can then enter the information into our formula to obtain: $F V = 75 ({1.025}^{12}) - 1 / 0.025$

$= 75 ({1.025}^{12}) - 1 / 0.025$

$= 75 (0.34488 . . . / 0.025)$

$= (0.34488 . . . \cdot 75) / 0.025$

$= 27.86666 . . . / 0.025$

$= 1034.66647$

$\sim 1034$

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