Mathematics, 02.03.2020 08:06 irene1806

How much should Sara deposit twice a year at 10% compounded semi-annually for 3
1/2 years to have a $15,000 down payment for her own restaurant?

Answers: 1

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Answers

Answer from: riahhrene

Step-by-step explanation:

Compound Interest

It's the type of financial calculations that includes the interest of previous periods into the new interests earned by some initial investment or principal P.

If we want to compute the final value FV of a series of n payments R at a fixed compound interest rate i, then

$FV=F_m\cdot R$

Where

$\displaystyle F_m=\frac{(1+i)^n-1}{i}$

The question provides us the following data

i=10% compounded twice a year

n=3 1/2 years

FV=15,000

We need to convert the number of periods and the interest rate to a semester base:

$\displaystyle i=\frac{10}{100\cdot 2}=0.05$

$n=3.5\cdot 2= 7\ semesters$

Let's calculate Fm

$\displaystyle F_m=\frac{(1+0.05)^7-1}{0.05}=8.142$

Knowing that

$FV=F_m\cdot R$

Solving for R

$\displaystyle R=\frac{FV}{F_m}=\frac{15,000}{8.142}=1,842.30$

Sara should deposit $1,842.30 twice a year to have the down payment for her own restaurant

Answer from: Quest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

←

add

94.09

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