137k views
4 votes
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?

User Keyu Gan
by
7.7k points

2 Answers

4 votes

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!

User Ryan Ward
by
8.6k points
5 votes

Answer:

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

User Nikolay Shebanov
by
8.3k points

Related questions

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories