Question

a.) A series of 25 end-of-year deposits beginning with $1390 at the end of year 1 and increasing by $410 per year with a 8% interest rate. What Uniform Series of deposits would result in the same cumulative balance?

b.) A series of 30 end-of-year deposits are made into an account that returns 4.2.% per year compounded annually. The first deposit is $5,251 and the deposits increase by 4.2% each year. How much will be in the account immediately following the 30th deposit?

Answer 1

a.) A series of 25 end-of-year deposits beginning with $1390 at the end of year 1 and increasing by $410 per year with a 8% interest rate. What Uniform Series of deposits would result in the same cumulative balance?

1^st year deposit = 1390

Increases by 410 (Gradient)

Rate of interest = 8%

Number of years = 25

Calculate Uniform Series of deposits

Uniform Series of deposits = A1 + G (A/G, 8%, 25)

Uniform Series of deposits = 1390 + 410 (8.22538) = 4762.40

Uniform Series of deposits will be $4762.40

b.) A series of 30 end-of-year deposits are made into an account that returns 4.2 % per year compounded annually. The first deposit is $5,251 and the deposits increase by 4.2% each year. How much will be in the account immediately following the 30th deposit?

Deposit in 1^st year = 5251 (A1)

Rate of interest = 4.2%

Deposit increases by = 4.2% (gradient)

Number of years = 30 years

Calculate the Future value of the deposits.

Calculate the PV of the above gradient series.

PV = A1 (N/1+i) (This formula of PV is used when the interest is equal to gradient)

PV = 5251 (30/1+.042) = 151,180

Calculating the FV of 151,180

FV = 151,180 (1+.042)^30 = 519,428.66