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earnstyle [38]
1 year ago
7

Merle Fonda opened a new savings account. She deposited $40,000 at 10% compounded semiannually. At the start of the fourth year,

Merle deposits an additional $20,000 that's also compounded semiannually at 10%. At the end of six years, what's the balance in Merle's account?
Mathematics
1 answer:
IrinaVladis [17]1 year ago
8 0
Use compound interest formula  F=P(1+i)^n twice, one for each deposit and sum the two results.

For the P=$40,000 deposit,
i=10%/2=5%  (semi-annual)
number of periods (6 months), n = 6*2 = 12
Future value (at end of year 6),
F = P(1+i)^n = 40,000(1+0.05)^12 = $71834.253

For the P=20000, deposited at the START of the fourth year, which is the same as the end of the third year.
i=5% (semi-annual
n=2*(6-3), n = 6 
Future value (at end of year 6)
F=P(1+i)^n = 20000(1+0.05)^6 = 26801.913

Total amount after 6 years
= 71834.253 + 26801.913
=98636.17   (to the nearest cent.)
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A park ranger spent $208 to buy 12 trees.
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Let x represent number of redwood trees and y represent number of spruce trees.

We have been given that a park ranger bought 12 trees. We can represent this information in an equation as:

x+y=12...(1)

y=12-x...(1)

We are also told that redwood trees cost $24 each, so cost of x redwood trees would be 24x.

Each spruce tree costs $16, so cost of y spruce trees would be 16y.

Since the park ranger spent $208 on trees, so we can represent this information in an equation as:

24x+16y=208...(2)

Upon substituting equation (1) in equation (2), we will get:

24x+16(12-x)=208

24x+192-16x=208

8x+192=208

8x+192-192=208-192

8x=16

\frac{8x}{8}=\frac{16}{8}

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Therefore, the park ranger bought 2 redwood trees.

Upon substituting x=2 in equation (1), we will get:

y=12-x\Rightarrow 12-2=10

Therefore, the park ranger bought 10 spruce trees.

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1 year ago
Gary spent $48 on a watch. He spent 1/3 of the remainder on a pen if he still had 1/2 of his money left,how much money did he ha
xeze [42]
T= total
<span>Money spent is: </span>
48+ 1/3 (T-48) = 1/2 T
One equation for one unknown, solve:

48 + 1/3 T -1/3*48= 1/2 T
48 - 16 =1/2 T- 1/3 T
32= 1/6 T
T= 6*32
<span>T=192

</span>192-48=144 money left after watch
1/3*144=48 third of leftover, spent on pen
<span>144-48=96 left which is half of 192. </span>
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Step-by-step explanation:

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