Question

Sandra deposits $3,000 at the end of each semiannual period for 12 years at 10% interest compounded semiannually. determine the amount she will have in the account after 12 years. round to the nearest cent. a. $133,506.00 b. $140,181.30 c. $121,291.43 d. $70,568.14

Answer 1

The amount Sandra will have in the account after 12 years is b. $140,181.30 if she deposits $3,000 at the end of each semiannual period

We can determine the amount she will have in the account after 12 years by using the formula for future value as follows;

FV = P(1+i)×{ (1+i)^n - 1 } / i

Here;

FV = future value of the money after n periods

P = deposit per period

i = interest rate per period

n = the number of periods

Substituting the values in this equation to find the amount after 12 years as follows;

FV = 3000(1+0.05)×( (1+0.05)^24 - 1 ) / 0.05

FV = 3000(1+0.05)×( (1+0.05)^23 ) / 0.05

FV = 140,181.296 = 140,181.30

Hence the amount after 12 years is calculated to be $140,181.30

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