Question

Parents wish to have 90000 available for a child's education. If the child is now 6 years old, how much money must be set aside at 3% compounded semiannually to meet their financial goal when the child is 18

Answer 1

To have $90,000 in 12 years at a 3% interest rate compounded semiannually, parents must set aside approximately $67,560.57 today.

Step-by-step explanation:

The question is asking how much money must be initially invested at a 3% interest rate compounded semiannually to accumulate $90,000 by the time the child turns 18, assuming the child is currently 6 years old. First, we have to determine the number of compounding periods, and then use the compound interest formula to find the present value of the future amount.

Since the child is 6 and the goal is to have the money by age 18, there are 12 years until the money is needed. Interest is compounded semiannually, so there are 2 compounding periods per year, which gives us a total of 12 years * 2 periods/year = 24 compounding periods.

The compound interest formula is:

A = P(1 + r/n)nt

We are given:

• Future Value (A) = $90,000
• Annual interest rate (r) = 3%, or 0.03
• Number of times interest is compounded per year (n) = 2
• Number of years (t) = 12

We're solving for the present value (P).

Rearranging the compound interest formula to solve for P:

P = A / (1 + r/n)nt

Plugging in the values:

P = $90,000 / (1 + 0.03/2)(2)(12)

Doing the math, we get:

P = $90,000 / (1.015)24 ≈ $67,560.57

Therefore, the parents need to set aside approximately $67,560.57 to meet their financial goal when the child is 18.

Answer 2

$62959

Step-by-step explanation:

We have been given that Parents wish to have 90000 available for a child's education. The child is now 6 years old. We are asked to find the amount of money that parents must set aside at 3% compounded semiannually to meet their financial goal when the child is 18.

We will use compound interest formula to solve our given problem.

`A=P(1+(r)/(n))^(nt)`, where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year.

t = Time in years.

`r=3\%=(3)/(100)=0.03`

`n=2`

`t=18-6=12`

`A=90000`

`90000=P(1+(0.03)/(2))^(2* 12)`

`90000=P(1+0.015)^(24)`

`90000=P(1.015)^(24)`

`90000=P(1.4295028119290251)`

`P=(90000)/(1.4295028119290251)`

`P=62958.952755\approx 62959`

Therefore, an amount of $62959 must be set aside to meet their financial goal when the child is 18.