Question

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

Answer 1

`A(n)=800(1+0.05)^(n-1); 972.41`

Explanation:

Principal = $800

Rate of interest = 5% = 0.05

Since we are given that At the beginning of year 1, Amada invests $800 at an annual compound interest rate of 5%.

Formula :

`A=P(1+r)^n`

A is the amount

P is the principal

r = rate of interest in decimal

n = times period

Since we are given that we need to find the amount at the beginning of year 5

So, we need to replace n with n-1

So, formula becomes :
`A=P(1+r)^(n-1)`

Substitute the values

`A(n)=800(1+0.05)^(n-1)`

`A(n)=800(1+0.05)^(5-1)`

`A(n)=972.41`

Hence Option A is correct.

`A(n)=800(1+0.05)^(n-1); 972.41`

Thus explicit formula can be used to find the account’s balance at the beginning of year 5 is
`A(n)=800(1+0.05)^(n-1)`

Balance at the beginning of year 5 is $972.41

Answer 2

1.
`A=800(1+0.05)^(n-1)` and $972.4

Explanation:

We are given that,

Investment in the first year = $800

Rate of interest = 5% = 0.05

As we know, the compound interest is given by
`A=P(1+r)^n`, 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
`A=800(1+0.05)^(n-1)`.

Further, when n= 5, we have,

`A=800(1+0.05)^(5-1)`.

i.e.
`A=800(1.05)^4`.

i.e.
`A=800* 1.2155`.

i.e. A= 972.4 dollars

Thus, the compounded value at the beginning of 5th year is $972.4

Hence, option 1 is correct.