Reagan has a savings account that earns 1.87% - id1871088732, amiraapplewell

Ответ:

kenoknox

13.03.2022

Mathematics

To solve this, we are going to use the compounded interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where

is the final amount after

years

is the initial investment

is the interest rate in decimal form

is the number of times the interest is compounded per year

is the time in years

We know from our problems that she needs $20,857 for a down payment on a house in 9 years, so A=20857

and

. To convert the interest rate to decimal form, we are going to divide the rate by 100%
$r= \frac{1.87}{100} =0.0187$
Since the interest is compounded quarterly, it is compounded 4 times per year; therefore, n=4

.
Lets replace the values in our formula to find

:
$A=P(1+ \frac{r}{n} )^{nt}$
$20857=P(1+ \frac{0.0187}{4} )^{(4)(9)}$
$P= \frac{20857}{(1+ \frac{0.0187}{4} )^{(4)(9)}}$
$P= \frac{20857}{(1+ \frac{0.0187}{4} )^{36}}$
P=17633.17

We can conclude that the correct answer is: B. 17,633.17

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Reagan has a savings account that earns 1.87% interest, compounded quarterly. if she needs $20,857 for a down payment on a house in 9 years, how much money will she need to invest in the account today? a. 10,704.95 b. 17,633.17 c. 19,355.32 d. 20,508.99

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