Question

1) Find the present value of $60,000 due in 5 years at the given rate of interest. (Use a 365-day year. Round your answer to the nearest cent.)

7%/year compounded daily

2) Use logarithms to solve the problem.

How long will it take $12,000 to grow to $15,000 if the investment earns interest at the rate of 3%/year compounded monthly? (Round your answer to two decimal places.)

3)The Pirerras are planning to go to Europe 4 years from now and have agreed to set aside $170/month for their trip. If they deposit this money at the end of each month into a savings account paying interest at the rate of 5%/year compounded monthly, how much money will be in their travel fund at the end of the fourth year? (Round your answer to the nearest cent.)

Answer 1

1) Find the present value of $60,000 due in 5 years at the given rate of interest.

7%/year compounded daily

Daily interest rate, r = 7%/365 = 0.0001917808219

Number of days, n = 5 * 365 = 1,825

PV = FV/(1 + r)^n

PV = 60,000/(1 + 0.0001917808219)^1,825

PV = 42,282.704256342

PV = $42,282.70

2) Use logarithms to solve the problem.

How long will it take $12,000 to grow to $15,000 if the investment earns interest at the rate of 3%/year compounded monthly?

r = 3%/12 = 0.0025

FV = PV * (1 + r)^n

(1 + r)^n = FV/PV

n ln(1 + r) = ln(FV/PV)

n = ln(FV/PV)/ln(1 + r)

n = ln(15,000/12,000)/ln(1 + 0.0025)

n = 0.2231435513/0.002496880199

n = 89.3689458507 months

or n = 89.3689458507/12= 7.4474121542 years

n = 7.45 years

3)The Pirerras are planning to go to Europe 4 years from now and have agreed to set aside $170/month for their trip. If they deposit this money at the end of each month into a savings account paying interest at the rate of 5%/year compounded monthly, how much money will be in their travel fund at the end of the fourth year?

r = 5%/12 = 0.004166666667

n = 4 * 12 = 48

The amount of money in the travel fund = $9,012.53

Can you please upvote? Thank you :-)