Question

ukaruhan Anna Krum plans to make 6 annual deposits of $12,500 cach into an account caming 7.5 percent (per year) compounded quarterly. If the first deposit is made today and the last deposit is made att how much will be in the account at t=8 if no more deposits were made after t-5? a. $111,338 1.5 1.5 1.575,10 b. $109,538 TIMO c. $122,549 g 1 2 3 4 5 6 d. $105,626 1,500 17,500 10,509 12,500 c. $113,773 *(1 + OK 24 - PM = 12,500 2.78133ņ =6 TY Il min mort FALSE2 7 s as years remaining

Answer 1

Compute the effective annual rate (EAR), using the equation as shown below:

EAR = (1 + {Rate/ Compounding periods}) ^{Compounding periods} – 1

         = (1 + {7.5%/4}) ⁴ – 1

         = 7.713586577%

Hence, the EAR is 7.713586577%.

Compute the PVIFA at 7.713586577% and 5 years, using the equation as shown below:

PVIFA = {1 – (1 + Rate)^{-Number of periods}}/ Rate

                   = {1 – (1 + 0.07713586577)^-5}/ 7.713586577%.

             = 4.02303264934

Hence, the PVIFA at 7.713586577% and 5 years is 4.02303264934.

Compute the PVIF at 7.713586577% and 8 years, using the equation as shown below:

PVIF = 1/ (1 + Rate)^{Number of periods}

              = 1/ (1 + 0.07713586577)⁸

         = 0.55186913326

Hence, the PVIF at 7.713586577% and 8 years is 0.55186913326.

Compute the value of investment after 8 years, using the equation as shown below:

Investment value = {Annual savings*(1 + PVIFA_{7.713586577%, 5 years})}/ PVIF_{7.713586577%, 8 years}

                             = {$12,500*(1 + 4.02303264934)}/ 0.55186913326

                             = $113,773

Hence, the value of investment after 8 years is $113,773.