Question

I need help plz someone help me solved this problem I need help ASAP! I will mark you as brainiest!

Answer 1

Answer:  (a) $\bold{A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}}$

               (b) A = $1680.67

               (c) t = 9.99 years

               (d) A = $1689.85

Step-by-step explanation:

$A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}$   where

• A is the amount accrued (balance)
• P is the principal (original/initial amount)
• r is the interest rate (convert to a decimal)
• n is the number of times compounded per year
• t is the number of years

a) Given: P = 900, r = 7% = 0.07, n = quarterly = 4

$\bold{A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}}$

b) Given: P = 900, r = 7% = 0.07, n = quarterly = 4, t = 9

$A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4(9)}\\\\\\A = 900\bigg(1+\dfrac{0.07}{4}\bigg)^{36}$

A = 1680.67

c) Given: A = 1800, P = 900, r = 7% = 0.07, n = quarterly = 4

$1800=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\2=\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\ln\ 2=ln\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\ln\ 2 = 4t\ ln\bigg(1+\dfrac{0.07}{4}\bigg)\\\\\\\dfrac{ln\ 2}{4\ ln\bigg(1+\dfrac{0.07}{4}\bigg)}=t\\\\\\\bold{t=9.99}$

d) $A=Pe^{rt}$

Given: P = 900, r = 7% = 0.07, t = 9

$A=900e^{0.07(9)}\\\\\\A=900e^{.63}\\\\\\\bold{A=1689.85}$