Mathematics, 22.10.2019 04:50 dodieoddle

76. currently, your savings for each month is capped at $400. if you start investing all of this into a savings plan earning 1% interest annually, compounded monthly, then how long will it take to save $160,000? (hint: use logarithms.)

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Answer from: pannita

10 years and 10 months.

Step-by-step explanation:

The annually interest rate (ia) can be converted by monthly (im) by the equation:

(1 + im)¹² = 1 + ia

(1 + im)¹² = 1 +0.01

(1 + im)¹² = 1.001 (putting ln in both sides)

ln(1 + im)¹² = ln1.001

12*ln(1 + im) = 1.0x10⁻³

ln(1 + im) = 8.33x10⁻⁵(applying "e in both sides)

$e^{ln(1 + im)} = e^{8.33x10^{-5}}$

1 + im = 1.00083

im = 0.00083 = 0.083%

For a investimenting, the final amount (A) can be calculated by:

$A = R*(\frac{(1+i)^n-1}{i} )$

Where R is the amount invested per month, i is the interest, and n the number of months:

160000 = 400 * $\frac{(1 +0.00083)^n - 1}{0.00083}$

$\frac{(1 +0.00083)^n - 1}{0.00083}$ = 400

1.00083ⁿ - 1 = 0.332

1.00083ⁿ = 1.332 (applying ln in both sides)

n*ln1.00083 = ln1.332

8.3x10⁻⁴n = 0.2867

n = 345.4 months

345.4 months *1 yea12 months = 10 years and 10 months.

Answer from: david3253

Ans. It wil take 346 months for you to save $160,000.

Step-by-step explanation:

Hi, well, first, we need to find the equivalent effective rate (effective monthly) of 1% compounded monthly, that is, dividing it by 12.

$r(e.m)=\frac{0.01}{12} =0.000833$

That is 0.0833% effective monthly, but we need to use the decimal representation in order to solve this problem. Now, we need to solve for "n" the following equation.

$Future Value=\frac{A((1+r)^{n} -1)}{r}$

Where:

Future Value= 160,000

A=400

r= 0.000833

The answer is going to be in months, since the annuity (periodic saving) is monthly and the rate is effective monthly. Let´s solve this equation.

$160,000=\frac{400((1+0.000833)^{n} -1)}{0.000833}$

$\frac{160,000*0.000833}{400} =(1.000833)^{n}$

$0.3332=1.000833^{n} -1$

$0.3332+1=1.000833^{n}$

$1.3332=1.000833^{n}$

Ln(1.3332)=n*Ln(1.000833)

$n=\frac{Ln(1.3332)}{Ln(1.000833)} =346$

So, it will take 346 months (nearly 29 years) for your savings account to reach $160,000.

Best of luck.

Answer from: Quest

i can not answer the question due to the fact that you spelled "carton" as "cartoon", a cartoon is something you watch on tv, a carton is a box that holds things. and also you've been waiting for this question for a while so why don't you get off your lazy a** and try to figure it out for yourself for once!

step-by-step explanation:

===============================================================^

look above, and leave your comments down below, and don't for get a five stars and a and brainliest xd

sorry for the stars in the middle of words its because it wouldn't let me submit. xd

How many cartoon of food an how many cartoons of clothing should be sent with each plane? including

Answer from: Quest

the answer is c

step-by-step explanation: i took a test with this question on it

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76. currently, your savings for each month is capped at $400. if you start investing all of this int...