# 735 at 7% for 2 1/2 years?

Jan 25, 2018

$A \approx \textcolor{red}{873.95}$

#### Explanation:

Assumed that interest is compounded half yearly.

Formula for total amount is

#A = P (1 + (r/n))^(nt) where

P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n = number of times the interest is compounded per year

Given : P = 735, r = 0.07, t = 5/2, n = 2

$A = 735 \cdot {\left(1 + \left(\frac{0.07}{2}\right)\right)}^{2 \cdot \left(\frac{5}{2}\right)}$

$A = 735 \cdot {\left(\frac{2.07}{2}\right)}^{5} \approx \textcolor{red}{872.95}$