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