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.

Step-by-step 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 + (r)/(n) )^n^t`

Solving for A₀:

`A_0 = (A(t))/((1+(r)/(n) )^n^t)`

Substituting the values:

`A_0 = (20000)/((1 + (0.0141)/(365))^3^6^5^X^1^8 ) \\\\A_0 = (20000)/(1.289)\\ \\A_0 = 15516`

Therefore, Adam should invest $15516 after 18 years.