Question

Jamal wants to save $54,000 for a down payment on a home. How much will he need to invest in an account with 8.8% APR, compounding daily, in order to reach his goal in 5 years? (Round your answer to the nearest cent.)

Answer 1

Answer:

The investment money in the account is $ 34785.96  

Step-by-step explanation:

Given as :

The amount after 5 years = $ 54,000

The rate of interest = 8.8 % compounded daily

The Time period = 5 years

Let the invested money = P

So, from compounded method

Amount = Principal × $(1+\dfrac{\textrm Rate}{365\times 100})^{365\times Time}$

$ 54,000 = P × $(1+\dfrac{\textrm 8.8}{365\times 100})^{365\times 5}$

Or, 54,000 = P × $(1.000241)^{1825}$

Or , 54,000 =  P × 1.55235

∴  P = $\frac{54000}{1.55235}$

I.e P = $ 34785.96

Hence The investment money in the account is $ 34785.96   answer

Answer 2

Using compound interest, it is found that he will need to invest $34,779.81.

Compound interest:

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

• A(t) is the amount of money after t years.  
• P is the principal(the initial sum of money).  
• r is the interest rate(as a decimal value).  
• n is the number of times that interest is compounded per year.  
• t is the time in years for which the money is invested or borrowed.

In this problem:

• Wants to save $54,000 in 5 years, thus $t = 5, A(t) = 54000$.
• Interest rate of 8.8%, thus $r = 0.088$.
• Daily compounding, thus $n = 365$.

• The amount he needs to invest is P.

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

$54000 = P(1 + \frac{0.088}{365})^{365(5)}$

$P(1.00024109589)^{1825} = 54000$

$P = \frac{54000}{(1.00024109589)^{1825}}$

$P = 34779.81$

He needs to invest $34,779.81.

A similar problem is given at https://brainly.com/question/24507395