MATH SOLVE

4 months ago

Q:
# At the beginning of year 1, Amada invests $800 at an annual compound interest rate of 5%. She makes no deposits to or withdrawals from the account.Which explicit formula can be used to find the account’s balance at the beginning of year 5? What is the balance? A(n) = 800 • (1 + 0.05)(n – 1); $972.41 B. A(n) = 800 + (n – 1)(0.05 • 800); $960.00 C. A(n) = 800 • (1 + 0.05)n; $1021.03 D. A(n) = 800 + (0.005 • 800)(n – 1); $1056.00

Accepted Solution

A:

Answer:1. [tex]A=800(1+0.05)^{n-1}[/tex] and $972.4Step-by-step explanation:We are given that,Investment in the first year = $800Rate of interest = 5% = 0.05As we know, the compound interest is given by [tex]A=P(1+r)^n[/tex], where P= initial amount, r= rate of interest and n= time period.Since, she has $800 in the 1st year. So, when n= 1, the compound value = $800.So, from these conditions, we get,Compound interest is [tex]A=800(1+0.05)^{n-1}[/tex].Further, when n= 5, we have,[tex]A=800(1+0.05)^{5-1}[/tex].i.e. [tex]A=800(1.05)^4[/tex].i.e. [tex]A=800\times 1.2155[/tex].i.e. A= 972.4 dollarsThus, the compounded value at the beginning of 5th year is $972.4Hence, option 1 is correct.