Question

Nicole is considering opening a Roth Individual Retirement Account. If she invests into the Roth IRA, determine the amount in the account if she makes annual payments of $4,291 into an account paying 2. 23% interest compounded annually for 30 years. A. $132,259. 66 b. $132,505. 45 c. $184,513. 76 d. $180,488. 86.

Answer 1

The future amount in the account (Roth IRA) is equal to: D. $180,488. 86.

Given the following data:

• Principal = $4,291

• Interest rate = 2.23%

• Time = 30 years

To determine the future amount in the account:

Mathematically, the compound interest for this Roth IRA is given by the formula:

$A = \frac{P(1\;+\;r)^t -1}{r}$

Where:

• P is the principal.

• r is the interest rate.

• t is the number of years.

• A is the future amount.

Substituting the given parameters into the formula, we have;

$A = \frac{4291(1\;+\;0.0223)^{30} -1}{0.0223}\\\\A = \frac{4291(1.0223)^{30} -1}{0.0223}\\\\A = \frac{4291(1.93798684094 -1}{0.0223}\\\\A = \frac{4291(0.93798684094)}{0.0223}\\\\A = \frac{4024.901534474}{0.0223}$

A = $180,488.86

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