Jessica received a gift of $7,500 at the time of her high school graduation.She invests it in an account that yields 10% compounded semiannually.What will the value of Jessica's investment be at the end of 5 years? (PV of $1,FV of $1,PVA of $1,and FVA of $1) $\bold{\text{(Use appropriate factor(s) from the tables provided.) }}$

A) $8,250.00
B) $11,250.00
C) $12,216.75
D) $9,375.00
E) $10,500.00

Question

Jessica received a gift of $7,500 at the time of her high school graduation.She invests it in an account that yields 10% compounded semiannually.What will the value of Jessica's investment be at the end of 5 years? (PV of $1,FV of $1,PVA of $1,and FVA of $1)

\bold{\text{(Use appropriate factor(s) from the tables provided.) }}

A) $8,250.00
B) $11,250.00
C) $12,216.75
D) $9,375.00
E) $10,500.00

Yolanda Lopez · Accepted Answer

Final Answer : C, Explanation :  We know that the principal (present value) Jessica invested is $7,500, the annual interest rate is 10% and the compounding period is semiannual. Therefore, the periodic interest rate is 5% (10% divided by 2) and the number of periods is 5 years multiplied by 2 semiannual periods per year, which is 10 periods in total.Using the compound interest formula: FV = PV x (1 + r)^n, where FV is the future value or ending balance, PV is the present value or principal, r is the periodic interest rate, and n is the number of periods.We can plug in the values and use the FV of $1 table for 5%, semiannually, and 10 periods to find the factor of 1.62889.FV = $7,500 x (1 + 0.05)^10FV = $7,500 x 1.62889FV = $12,216.75Therefore, the value of Jessica's investment at the end of 5 years is $12,216.75. The correct answer choice is C.

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