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

Question

Mathematics

Kate Harrell

9 June, 14:06

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

+3

Answers (1)

Know the Answer?

Brayan Chang · Answer 1

Annuity formula for depositing at the end of each period. Future value, F=A * ((1+i) ^n-1) / iA=deposit per period, $3000 i=interest per period, 10%/2 = 5% = 0.05 per half yearn=number of periods = 12 years = 24 half-years

If the deposit is at the beginning of each period, thenwe can use the above formula, with 25 periods, but skipping the final payment, i. e. F=A * ((1+i) ^ (n+1) - 1) / i-A=3000 * ((1+.1/2) ^ (24+1) - 1) / (.1/2) - 3000=143181.296 - 3000=143181.30 - 3000=140181.30 (to the nearest cent)