Question

Sam deposited money into an account in which interest is compounded semiannually at a rate of 1.25%. How much did she deposit if the total amount in her account after 7 years was $4115.73, and she made no other deposits or withdrawals?

Answer 1

Answer: 3771.94

Step-by-step explanation:

(1+0.0125/2)^14 = 1.091145

You get the 2 from the semiannually

and the 14 came from doing 7 x 2

and you move the decimal 1.25% to the left twice, to get 0.0125

Then you take $4115.73 and divide that by 1.091145

4115.73/1.091145 = 3771.94

and I took the test and got it right!

Answer 2

Answer:

The total amount deposited is $$3771.94$

Step-by-step explanation:

Topic: Compound Interest

We'll solve this question using compound interest formula. The formula is as follows:

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

Where

r = Rate = 1.25% = 0.0125

n = Period = Semiannually = 2

t = Time = 7 years

A = Amount = $4115.73

P = Principal Amount ---- This is what we are solving for

By Substitution, we have

$4115.73 = P(1 + \frac{0.0125}{2} )^{2*7}$

$4115.73 = P(1 + 0.00625 )^{14}$

$4115.73 = P(1.00625 )^{14}$

$4115.73 = P(1.09114510137)$

$P =\frac{4115.73}{1.09114510137}$

$P = 3771.93646826$

The total amount deposited is $$3771.94$ --- Approximated