In: Economics
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?
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?
1st 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 1st 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