note: please make sure to properly format your answers. all dollar figures in the answers need to include…

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to decimal places, show both decimal places (5.06). when abram was born, his parents put $2,000 into an account that yielded 1.2% interest, compounded semi - annually. when he turns 16, his parents will give him the money to buy a car. how much will abram receive on his 16th birthday?

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to decimal places, show both decimal places (5.06). when abram was born, his parents put $2,000 into an account that yielded 1.2% interest, compounded semi - annually. when he turns 16, his parents will give him the money to buy a car. how much will abram receive on his 16th birthday?

Answer

Explanation:

Step1: Identifier les paramètres

$P = 2000$ (montant initial), $r=0.012$ (taux d'intérêt annuel), $n = 2$ (composant semi - annuellement), $t = 16$ (années)

Step2: Appliquer la formule du capital - composé

La formule du capital - composé est $A=P(1 + \frac{r}{n})^{nt}$. On remplace les valeurs : $A = 2000(1+\frac{0.012}{2})^{2\times16}$

Step3: Calculer l'exposant

$2\times16 = 32$ et $\frac{0.012}{2}=0.006$. Donc $A = 2000(1 + 0.006)^{32}$

Step4: Calculer la valeur entre parenthèses élevée à la puissance

$(1 + 0.006)^{32}\approx1.210906$.

Step5: Calculer le montant final

$A=2000\times1.210906=$2421.81$

Answer:

$$2421.81$