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

The total amount deposited is $
`3771.94`

Explanation:

Topic: Compound Interest

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

`A = P(1 + (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 + (0.0125)/(2) )^(2*7)`

`4115.73 = P(1 + 0.00625 )^(14)`

`4115.73 = P(1.00625 )^(14)`

`4115.73 = P(1.09114510137)`

`P =(4115.73)/(1.09114510137)`

`P = $3771.93646826`

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