Question

Natalie and Preston would like to accumulate $25,000 at the end of 3.5 years for a future down payment on a house in Prescott. How much should they deposit at the end of each week in a savings account that pays 7.2%/a compounded monthly to meet their goals?

Answer 1

$7.4 should be deposited at the end of each week

Explanation:

In this question, we are asked to calculate the principal amount that should be deposited to get a house of $25,000 at the interest and time given in the question

To solve this problem, we use the compound interest formula.

Mathematically;

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

From the question, we identify the following;

A is the amount that is targeted which is the principal plus the targeted interest = $25,000 according to the question

P is the amount invested at the beginning which we are looking for

r is the rate which is 7.2% = 7.2/100 = 0.072

n is the number of times we compound per year which is 12 times( compounding is per month)

t is the number of years which is 3.5 years

To get the principal, we can rewrite the equation to be;

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

25,000/(1 + 0.072/12)^(12 * 3.5) = P

P = 25,000/18.54 = $1,348

But the question asks how much to be deposited at the end of each week

The number of weeks in 3.5 years is 3.5 * 52 =182 weeks

Thus, the amount deposited at the end of each week will be 1,348/182 = $7.4