Question

Albert deposited x dollars into a new account that earned 6.5% annual interest, compounded annually. One year later, Albert deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of those two years, find an expression for x in terms of w, x(w).

Also describe

Answer 1

x(w) = w/2.2

Explanation:

The formula for accrued amount given an initial value of P and an annual interest rate of R% compounded annually for t years:

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

where r is interest rate in decimal = R/100

and t = number of years

r = 6.5/100 = 0.065

Hence, after 1 year

`A = x(1+0.065)^1\\\\ A = x(1.065)\\\\ A = 1.065x`

At the end of the first year, an additional amount of x was deposited

Total amount at end of year 1 = A + x

= 1.065x + x = 2.065x

After one more year, the amount would be
2.065x(1.065x) =

We are given that this amount accrues to w at end of year 2

= 2.199225x ≈ 2.2x

We are given this amount is w
Hence w = 2.2x
x(w) = w/2.2