Question

You save 8,500.00 you place 40% in a saving account earning a 4.2 APR compounded annually and the rest in a stock plan. the stock plan decreases 3% in the first year and increase in the second year

1. what is the total gain at the end of the second year for both accounts combined ? 509.63

2. If you had invested 60% in the savings account and the rest in the stock plan, what is the difference in the total gain compared to the original? 73.12

I already know the answers to both since my teacher gave it to me, but now i need to explain the step by step procedures on how to get that answer.

Answer 1

The question is not complete,find below complete question:

You save $8,500.00. You place 40% in a savings account earning a 4.2% APR compounded annually and the rest in a stock plan. The stock plan decreases 3% in the first year and increases 7.5% in the second year. What is the total gain at the end of the second year for both accounts combined?

A. $505.14

B. $509.63

C. $442.18

D. $474.31

B is the correct option

Explanation:

The amount placed in savings =40%*8500=3,400

Amount placed in stock plan=8500-3400=5,100

The amount in stock account at end of year=5,100*(1-3%)=4947

The amount in stock account at end of year two=4947 *(1+7.5%)= 5,318.03

The amount in savings account in year two can be computed using the future value formula below

fv=pv*(1+r)^n

pv is the initial amount of 3,400

r is the annual APR of 4.2%

n is the number of years 2

fv=3,400*(1+4.2%)^2= 3,691.60

Gain from savings = 3,691.60-3400=291.6

gain from stock plan= 5,318.03-5100 =218.03

total gains=218.03 +291.6=509.63

60% invested in savings account:

The amount placed in savings =60%*8500=5,100

Amount placed in stock plan=8500-3400=3,400

The amount in stock account at end of year=3400*(1-3%)=3298

The amount in stock account at end of year two=3298 *(1+7.5%)=3545.35

The amount in savings account in year two can be computed using the future value formula below

fv=pv*(1+r)^n

pv is the initial amount of 5,100

r is the annual APR of 4.2%

n is the number of years 2

fv=5100*(1+4.2%)^2= 5,537.40

Gain from savings = 5,537.40 -5100=437.4

gain from stock plan= 3545.35 -3400=145.35

total gains=145.35 +437.4=582.75

Difference in gains=582.75 -509.63 =73.12

Answer 2

Answer: A.) $509.64

B.) 73.12

Explanation:

Saved amount = $8500

Savings account = 0.4 × 8500 = $3400; rate(r)= 4.2%, composed annually.

Stock plan = 8500 - 3400 = $5100

Using compound interest formula for the amount in a savings account :

Period(t) =2

A = P(1 + (r÷n))^nt

A = 3400(1 + (0.042 ÷ 1))^(1×2)

A= 3400( 1 + 0.042)^2

A = 3400(1.042)^2

A = $3691.60

gain on saving = 3691.60 - 3400= $291.60

Stock plan:

First year = 3% decrease

5100(1-0.03) = $4947

Second year = 7.5% increase

4947(1+0.075) = $5318.03

Gain on stock = $5318.03 - $5100 = $218.03

Total profit = $218.03 + $291.60 = $509.63

B.) If 60% had been to savings :

Savings account = 0.4 × 8500 = $5100; rate(r)= 4.2%, composed annually.

Stock plan = 8500 - 5100 = $3400

Using compound interest formula for the amount in a savings account :

Period(t) =2

A = P(1 + (r÷n))^nt

A = 5100(1 + (0.042 ÷ 1))^(1×2)

A= 5100( 1 + 0.042)^2

A = 5100(1.042)^2

A = $5537.386

gain on saving = $5537.386 - 5100= $437.386

Stock plan:

First year = 3% decrease

3400(1-0.03) = $3298

Second year = 7.5% increase

3298(1+0.075) = $3545.35

Gain on stock = $3545.35 - $3400 = $145.35

Total profit = $437.386 + $145.35 = $582.73

PROFIT difference = $582.736 - 509.63 = $73.106