Question

Paul and Susan are planning a trip to Greece and they want to save for this trip. They will need RM12,000 for each person at the end of four years. Both of them can invest a certain amount together at the beginning of each of the next four years in a bank account that will pay 6.8 percent annually.

Required:

Calculate the total amount they need and how much they will have to invest annually to reach their target?

Answer 1

Amount that Paul and Susan needs after 4 years for their trio to Greece=$12,000/person

They will invest certaian amount together at starting of each year

Interest to be paid by the bank on these deposits annulay=6.8%

First Part of the question: Total amount they need after 4 years =2*12,000=RM 24,000

Second part:

Investments to be made at start of every year for next 4 years:

Let the investment be X

so after Year 1 this amount becomes=X*(1+0.068), and Similarly,

at th end of Year 2 amount becomes=[ X*(1+0.068)^2+X*(1+0.068)]

at th end of Year 3 amount becomes=[ X*(1+0.068)^3+X*(1+0.068)^2+X*(1+0.068)]

at th end of Year 4 amount becomes=[ X*(1+0.068)^4+X*(1+0.068)^3+X*(1+0.068)^2+X*(1+0.068)]

Now this amount should be equal to RM 24,000

[ X*(1+0.068)^4+X*(1+0.068)^3+X*(1+0.068)^2+X*(1+0.068)]=24,000(At the end of 4th year)

X*4.727834=24,000

X=RM 5,076.321

Hence they have to make together RM 5,076.321 per year for next 4 years to get RM 24,000