Question

a $1,600 principal earns 7% annual interest, compounded semiannually (twice per year). After 33 years, what is the balance in the account?

Answer 1

Given is the Principal amount, P = 1600 dollars.

Given the Annual interest is 7% i.e. r = 0.07

Given the Compounding period is semi-annually i.e. n = 2.

Given is the Time of investment, t = 33 years.

It says to find the Final Value of invested amount in the account after 33 years.

We know the formula for Future Value of Money is given as follows :-

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Hence, the final balance would be 15,494.70 dollars.

Answer 2

After 33 years balance in the account = A= $15494.696

Step-by-step explanation:

We will applying the compound interest formula.

`A =  P(1 +(r)/(n))^(nt)`

Where,

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years

Given that,

P = $1,600

r = 7% =
`(7)/(100)` = 0.07

n = 2 (because of twice in a year)

t = 33 years

A=
`1600(1 + (0.035)/(2)) ^(2*33)`

A =
`1600 (1.035)^(66)`

A= $15494.696