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Korvikt [17]
3 years ago
8

Jacques deposited $1,900 into an account that earns 4% interest compounded semiannually. After t years, Jacques has $3,875.79 in

the account. Assuming he made no additional deposits or withdrawals, how long was the money in the account?
Compound interest formula:v(t)=p(1+r/n)^nt

t = years since initial deposit
n = number of times compounded per year
r = annual interest rate (as a decimal)
P = initial (principal) investment
V(t) = value of investment after t years
Business
2 answers:
kupik [55]3 years ago
3 0
A year has two semesters, then
n = 2<span>v(t)=p<span><span>(<span>1+<span>r/2</span></span>)</span><span>2t
</span></span></span><span>
3875.79 = 1900∗<span><span>(<span>1+(<span>0.04/2)</span></span>)^</span><span>2t
</span></span></span><span>
2.0398895 = <span><span>(<span>1+<span>0.042</span></span>)^</span><span>2t
</span></span></span>Apply natural logarithm on both sides

<span>ln(2.0398895) = ln<span>[<span><span>(<span>1+<span>0.042</span></span>)^</span><span>2t</span></span>]

Then simplify,
</span></span><span>0.712896 = 2t∗ln(1.02)

</span><span>t = <span>0.712896 / (<span>2∗ln(1.02))
</span></span></span><span><span>
t=18 years

I hope my answer helped you. Have a nice day!</span></span>
yarga [219]3 years ago
3 0

Answer:

18 years

Explanation:

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I want to have a college fund for my daughter. She is 5, so I have 13 years to achieve my goal of $50,000. The bank says I can e
Tju [1.3M]

Answer:

$2960 yearly savings

Explanation:

From the values given and from mathematical manipulation, he or she needs a contribution of at least $2900 every year in order to achieve his goal of $50,000.

                     EXPLANATION

  • If the child is 5yr old now, in 13years time, she will be 18yr old.
  • $2950 target yearly

  • for the next 13years, it would have amount to $38350

  • remember the bank will give an annual interest rate of 2%
  • so for 13years, that's 26% = 0.26

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3 0
3 years ago
What is the acceleration of an object that has a mass of 4.0 kg if the net force acting on it is 26N
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The current rates for an 80/20 mortgages are 4.15% for the first mortgages and 9.75% for the second mortgage. On a $200,000 30 y
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Answer: The actual rate of the mortgage is 5.27%.

Since we're taking two mortgages for a total of $200,000 for 30 years, we can find the actual rate of the mortgage by finding the weighted average of the two rates. The weights in this case will be the proportion of loan taken at each rate

We have

Rates       Weights      Rates * Weights

4.15            0.80     4.15 * 0.80 = 3.32

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Total                                             5.27%  

5 0
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