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lapo4ka [179]
2 years ago
12

Sylvia set a goal of saving at least $200 in a savings account.

Mathematics
2 answers:
lana [24]2 years ago
8 0

Answer:

twenty eight more weeks till$200

Katyanochek1 [597]2 years ago
3 0
So she needs to save 200 she has 60 in the account she invests 5 per let’s use x as a variable so she invests 5 per x weeks until she reaches 200 hope this helps
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F(x) = 3x + 8<br> Inverse function?
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2. Harry just deposited $1500 into a savings account giving 6% interest compounded quarterly.a) How much will be in the account
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The formula for compound interest is:

\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ A=\text{ Final amount} \\ r=\text{ Interest rate} \\ n=\text{ Number of times interest applied per period} \\ t=\text{ Number of time period elapsed} \\ P=\text{ Intial principal balance} \end{gathered}

Given data:

\begin{gathered} P=\text{ \$1500} \\ r=6\text{ \%}=0.06 \\ n=4\text{ times (compounded quarterly)} \end{gathered}

a. After ten years, that is t = 10 years, the amount in the account will be

\begin{gathered} A=1500(1+\frac{0.06}{4})^{4\times10} \\ A=\text{ }1500(1+0.015)^{40} \\ A=\text{ }1500(1.015)^{40} \\ A=\text{ \$2721.03} \end{gathered}

b. After twenty years, that is t = 20 years, the amount in the account will be:

\begin{gathered} A=1500(1+\frac{0.06}{4})^{4\times20} \\ A=1500(1.015)^{4\times20} \\ A=1500(1.015)^{80} \\ A=\text{ \$}4935.99 \end{gathered}

c. The time it takes for Harry's initial account value to double will be:

\begin{gathered} A=2\text{ x initial value = 2 }\times\text{ \$1500 = \$3000} \\ 3000=1500(1.015)^{4t} \\ (1.015)^{4t}=\frac{3000}{1500} \\ (1.015)^{4t}=2 \\ \text{ Find the logarithm of both sides} \\ \ln (1.015)^{4t}=\ln 2 \\ 4t=\frac{\ln 2}{\ln 1.015} \\ 4t=46.56 \\ t=\frac{46.56}{4}=11.64 \end{gathered}

Therefore, the time it takes Harry's initial account to double is approximately 11 years

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Step-by-step explanation:

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