7. keith wendell plans to borrow $5,810. he has decided on a term of 95 days at 8% interest. he has a choice of two lenders. one calculates interest using a 360-day year and the other uses a 365-day year. find the amount of interest wendell will save by using the lender with the 365-day year. $1.54 $1.67 $1.63 $1.68 8. jake winters plans to invest $7,400. find the interest rate required for the fund to grow to $7,844 in 8 months. 9% 5.7 % 8.5% 6%

Given:
Principal : $5,810
term: 95 days
rate: 8%

365/360 days

Interest = Principal * rate * term
Interest = 5,810 * 0.08 * 95/360
Interest = 122.66

Interest = 5,810 * 0.08 * 95/365
Interest = 120.98

122.66 - 120.98 = 1.68

Wendell will save $1.68 in interest if he chose the lender that uses 365-day year.

Given:
Principal - $7,400
Future Value - 7,844
term - 8 months
interest rate - x

Interest = 7844 - 7400 = 444

Interest = Principal * rate * term
444 = 7,400 * rate * 8/12
444 = 4,933.33 * rate
444 / 4,933.33 = rate
0.09 = rate

The interest rate required for the fund to grow to $7,844 in 8 months is 9%

a) E(X) = $7.4124

b) Standard deviation = $277.1

Step-by-step explanation:

P(X=xᵢ) = pᵢ

P[X=winning the car($32000)]= 1/13320 = 0.000075

P[X=winning the gas card($175)] = 1/13320 = 0.000075

P[X=winning the shopping car($5)] = 13318/13320 = 0.99985

Expected value is given by

E(X) = Σ xᵢpᵢ

E(X) = (32000 × 0.000075) + (175 × 0.000075) + (5 × 0.99985) = $7.412375 = $7.4124

b) Standard deviation = √(variance)

But Variance = Var(X) = Σx²p − μ²

where μ = E(X) = 7.4124

Σx²p = (32000² × 0.000075) + (175² × 0.000075) + (5² × 0.99985) = 76,827.29

Var(X) = 76,827.29 - 7.4124² = 76,772.349

Standard deviation = √(76,772.349) = $277.1