Ask question

Ask question

All categories

2 years ago

10

A Roth IRA is advertised to pay 1.5% annual interest. You researched the rate of inflation to be 1.15% this year. What is the ac

tual or real rate of return on the IRA?

1 answer:

jekas [21]2 years ago

3 0

Answer: 0.35%

Step-by-step explanation:

Given the following :

Advertised interest rate = nominal rate = 1.5%

Inflation rate = 1.15%

The real rate of return is calculated by:

[(1 + nominal rate) / ( 1 + inflation rate)] - 1

[(1 + (1.5/100)) / (1 + (1.15/100))] - 1

[(1 + 0.015) / ( 1 + 0.0115)] - 1

[ 1.015 / 1.0115] - 1

1.0034602 - 1 = 0.0034602

Real rate of return = (0.0034602 * 100)%

Real rate of return = 0.346%

You might be interested in

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

1 year ago

At a summer camp, there are 15 counselors, 5 cooks, and 120 campers. 5 points

lesya [120]

Answer:

eto 1:12 pero di ko sure,antayin mo nlng yung sagot ng iba

8 0

2 years ago

Ow many decimals numbers are there whose value equals the average of their digits?

kiruha [24]

Answer:

Step-by-step explanation:

there are infinite numbers between 2 and 3 having average=2.5

2.49,2.51

2.48,2.52

2.47,2.53

2.46,2.54

.................

2.491,2.509

2.492,2.508

2.493,2.507

......................

6 0

1 year ago

Which are rational and irrational? Thanks in advance :)

DochEvi [55]

Answer:

$3\frac{1}{2}-rational$

$\pi -irrational$

$-\frac{2}{3}-rational$

$\sqrt{16} -rational$

$\sqrt{3} -irrational$

$18-rational$

$0.625-rational$

$0.987987987...-rational$

Step-by-step explanation:

Rational numbers:

-are all numbers you can write as a quotient of integers $\frac{a}{b}$ , $b\neq 0$

-include terminating decimals. For example, $\frac{1}{8}=0.125$

-include repeating decimals. For example, $\frac{1}{3} =0.33333....$

Irrational numbers:

-have decimal representations that neither terminate nor repeat. For example, $\sqrt{2}=1.414213....$

-cannot be written as quotients of integers

8 0

2 years ago

Can anyone help me please, if you see this and willing to help me with something say yes! thank you. have great day!

malfutka [58]

Answer:

I am willing to help, just send your problems in the comments!

Step-by-step explanation:

You can send the problem in the comments or create a separate question.

6 0

1 year ago