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solniwko [45]
3 years ago
13

(10000*C)/1.05+(10000*C)/1.05^2…..(10000*C)/1.05^13=100 Find C?

Mathematics
1 answer:
rosijanka [135]3 years ago
3 0

9514 1404 393

Answer:

  C ≈ 0.00106455765168

Step-by-step explanation:

This is the sum of 13 terms of the geometric series that has 10000C/1.05 as the first term and a common ratio of 1/1.05. The sum S is given by ...

  S = a1(1 -r^n)/(1 -r) . . . . a1 is the first term, r is the common ratio

Using the known values, we have ...

  100 = (10000C/1.05)(1 -1.05^-13)/(1 -1/1.05))

  0.01 = C(1 -1.05^-13)/0.05

  C = 0.0005/(1 -1.05^-13) ≈ 0.0005/0.469679

  C ≈ 0.00106455765168

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If I deposit $400 each month into an account earning 8% interest compounded monthly, I will have $6,517 in my account in 35 years. The total money that I will put into the account is $168,000. I will earn a total compound interest of $6,117.

  • Calculating the Sum of Money in 35 years

Given information is as follows,

Principal, P = $400

Rate = 8%

Time, T = 35 years

n = 12 (Compounded monthly)

The amount for compound interest is given as,

A = P\frac{(1+\frac{R}{n} )^{nT} -1}{R/n}

A = 400\frac{(1+\frac{0.08}{12} )^{12.35} -1}{0.08/12}

A = 6,517.02

A = $6,517 (to the nearest cents)

  • Calculating the Amount Put in Account

Since, $400 is deposited every month for 35 years,

Amount Put in 35 years for this compound interest =$400 × 12 × 35

= $168,000

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A = P + CI

Thus, the compound interest is given by,

CI = A - P

CI = 6517 - 400

CI = $6,117

I will earn a total interest of $6,117

Learn more about compound interest here:

brainly.com/question/14295570

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Simplifying 10/15, the answer is

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