# Beatrice invests $1,450 in an account that pays 4 percent simple interest. How much more could... ## Question: Beatrice invests$1,450 in an account that pays 4 percent simple interest. How much more could she have earned over a 5-year period if the interest had compounded annually?

a) $35.16 b)$24.15

c) $20.32 d)$28.12

e) 120.73 ## Present value Present value refers to the estimated equivalent present amount of the sum of the money in the future by discounting based on the stated interest rate. ## Answer and Explanation: The following formula can be used to calculate the difference of the interest earned. {eq}Interest~earned=\bigg[PV*(1+k)^{n}\bigg]-\bigg[(PV*r*n)+PV\bigg]\\ whereas:\\ PV=present~value\\ r=simple~interest~rate\\ n=number~of~periods\\ k=compounded~interest~rate\\ {/eq} {eq}\begin{align*} Interest~earned&=\bigg[1,450*(1+.05)^{5}\bigg]-\bigg[(1,450*.04*5)+1,450\bigg]\\ &=(1,450*1.216653)-(290+1,740)\\ &=1,764.15-1,740\\ &=24.15 \end{align*} {/eq} Beatrice would earned an extra B.24.15 if she invested it in an accounts which compound annually 