Question

In: Economics

B. A series of 25 end-of-year deposits beginning with $1135 at the end of year 1...

B. A series of 25 end-of-year deposits beginning with $1135 at the end of year 1 and increasing by $260 per year with a 6% interest rate. What Uniform Series of deposits would result in the same cumulative balance? $

C. John makes 35 end-of-year deposits into a retirement account that returns 5.0.% per year compounded annually. His first deposit is $7500 and he increases the deposits by 8.9% each year. How much will be in the account immediately following the 35th deposit? $

Expert Solution

B. A series of 25 end-of-year deposits beginning with $1135 at the end of year 1 and increasing by $260 per year with a 6% interest rate. What Uniform Series of deposits would result in the same cumulative balance?

Answer –

Cash flow in the 1^st year – 1135 (A1)

Increases by 260 per year (Gradient)

Rate of Interest – 6%

Calculate the Uniform Series deposits.

Annual Cash flow = A1 + G (A/G, 6%, 25)

Annual Cash flow = 1135 + 260 (9.0722)

Annual Cash flow = 3494

C. John makes 35 end-of-year deposits into a retirement account that returns 5.0% per year compounded annually. His first deposit is $7500 and he increases the deposits by 8.9% each year. How much will be in the account immediately following the 35th deposit?

Answer –

Cash flow in the 1^st year – 7500 (A1)

Increases by 8.9%

Number of years – 35

Rate of interest – 5%

PW of the geometric gradient series = A1 (1 – (1+g)^n (1+i)^-n) ÷ i – g

PW of the geometric gradient series = 7500 (1 – (1+.089)^35 (1+0.05)^-35) ÷ .05 - .089

PW = 496,884

Future Value at 35^th year = 496,884(1+i)^35

Future Value at 35^th year = 496,884(1+.05)^35

Future Value at 35^th year = 2,740,820 (Approx)

Rahul Sunny answered 2 years ago

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