Answer: A.) $509.64
B.) 73.12
Step-by-step 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
