Question

Adam wishes to have ​$20 comma 000 available in 18 years to purchase a new car for his son as a gift for his high school graduation. To accomplish this​ goal, how much should Adam invest now in a CD that pays 1.41​% interest compounded quarterly​?

Answer 1

Adam should invest $15516 after 18 years.

Explanation:

Given:

Amount(18) = $20000

Rate of Interest, r = 1.41%

Time, t = 18 years

n = 365 (compounded daily)

General equation of amount that is compounded daily:

$A(t) = A_0(1 + \frac{r}{n} )^n^t$

Solving for A₀:

$A_0 = \frac{A(t)}{(1+\frac{r}{n} )^n^t}$

Substituting the values:

$A_0 = \frac{20000}{(1 + \frac{0.0141}{365})^3^6^5^X^1^8 } \\\\A_0 = \frac{20000}{1.289}\\ \\A_0 = 15516$

Therefore, Adam should invest $15516 after 18 years.