Suppose someone wants to 6% Plan B is a single depost into an account win contin

Question

Suppose someone wants to 6% Plan B is a single depost into an account win continuous accumulate $120 000 for retrement in 30 years The person has two choices. Plan A is a single deposit into an account with annual compounding and an APR of compoundng and an APR of 5 6% How much does the person need to depost n each account in order to reach the goarn The person must depost $ 20003 22 into the account for Plan A to reach the goa of $120,000 Round to the nearest cent as needed ) The person must deposdinto the account for Pian B to reach the goal of $120,000 Round to the nearest cent as needed le

Explanation / Answer

1) Given that the the amount to be accumulated after 30 years(t) is $120,000(A). This has to be done through a single deposit P, with continous compounding. Here APR is equivalent to interest rate, so r = 6%

Formula for continous compounding is A = Pert => 120000 = P e0.06*30 => 120000 = P(6.05)

=> P = $19,834.71

2)

-$200+$51.74+60+1.04=-87.22

(if Payment is maid)

or

$51.74+60+1.04= $112.78

(Amount needed to pay-off the debt completely)

So at the end of the 11th month, we have the debt paid off.

c) Mitch was depositing $1100 per year, for 10 years, which has an average annual return is 7%.

So P = $1100, t=10 years, r=7%.

So, the amount the the end of 10th year is the future value of annuity. So formula for future value of annuity is

A = P((1+i)t1 -1)/i = 1100((1+0.07)10-1)/0.07 = $15,198.09

This amount A is then compounded every year for the next 43 years, therefore the future value of A = A(1+r)t2

=> A = (15198.09)(1+0.07)43 = $ 278,799.21.

At age 75, Mitch has $278,799.21 in his account.

Month Payment Expenses Interest New Balance 0 $1300 1 $200 $60 0.02*$1300= $26.00 $1300-$200+$60+$26.00 =$1186.00 2 $200 $60 0.02*$1186= $23.72 $1186-$200+$60-$23.72 =$1069.72 3 $200 $60 0.02*$1069.72= $21.39 $1069.72-$200+$60-$21.39 =$951.11 4 $200 $60 0.02*$951.11= $19.02 $951.11-$200+$60-$19.02=$830.14 5 $200 $60 0.02*$830.14 =$16.60 $830.14-$200+$60+16.60 = $706.74 6 $200 $60 0.02*$706.74= $14.14 $706.74-$200+$60+$14.14 = $580.88 7 $200 $60 0.02*$580.88= $11.62 $580.88-$200+$60+$11.62 =$452.50 8 $200 $60 0.02*$452.50 =$9.05 $452.50-$200+$60+$9.05 =$321.55 9 $200 $60 0.02*$321.55 =$6.43 $321.55-$200+$60+$6.43 =$187.98 10 $200 $60 0.02*$187.98 =$3.76 $187.98-$200+$60+$3.76 = $51.74 11 $200 $60 0.02*$51.74 =$1.04

-$200+$51.74+60+1.04=-87.22

(if Payment is maid)

or

$51.74+60+1.04= $112.78

(Amount needed to pay-off the debt completely)

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