Respuesta :
Answer:
1) 3.7 years
2) $2,448.89
Explanation:
1. Amount in bank = $3,400
Return, r = 11% = 0.11
Future value = $5,000
Now,
Future value = Principle × ( 1 + r )ⁿ
here,
n is the time
$5,000 = $3,400 × ( 1 + 0.11 )ⁿ
or
1.4706 = 1.11ⁿ
taking log both sides
log(1.4706) = log(1.11ⁿ)
also,
log(aᵇ) = b × log(a)
Thus,
log(1.4706) = n × log(1.11)
0.1675 = n × 0.0453
or
n = 3.69 ≈ 3.7 years
2) Amount to repay = $3,000
Interest = 7% = 0.07
Time, n = 3 years
Now,
Future value = Principle × ( 1 + r )ⁿ
or
$3,000 = Principle × ( 1 + 0.07 )³
or
$3,000 = Principle × 1.225043
or
Principle = $2,448.89
Hence,
Amount to be set aside = $2,448.89
1) With an investment account of $3,400 yielding returns of 11% per year, it will take your 3.7 years to make $5,000 down payment on the car.
2) To pay off the loan of $3,000 in three years at 7%interest, you need to have $2,448.89 in your account currently.
Data and Calculations:
1) I/Y (Interest per year) = 11%
PV (Present Value) = $3,400
PMT (Periodic Payment) =$0
FV (Future Value) =$5,000
Results:
N (# of periods) = 3.7 years
Total interest = $1,600
2) N (# of periods) = 3 years
I/Y (Interest per year) = 7%
PMT (Periodic Payment) = $0
FV (Future Value) = $3,000
Results:
PV = $2,448.89
Total Interest = $551.11
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