Question

You want to have 7,000 euros in your savings account after 6 years. If bank is ready to accrue 5% on this account, how much money should be invested?

Answer 1

At the end of 6 years, we want to have 7,000 euros in our savings bank account.

No of years = n = 6 years

Amount at the end of 6 years (investment period) = P1 = 7,000 euros.

The bank is ready to accrue 5% on this account. Since compounding frequency is not mentioned, we assume it to be 1 year.

Thus time periods = t = n*1 = 6.

(Note: if it was, say, quarterly compounded, then there were 4 periods in 1 year and t would have been 6*4 = 24 in that case)

Annual interest rate = i = 5%

Let the amount to be invested be P.

P1 = P*[(1 + i)^t]

7,000 = P*[1.05^6]

Thus, P = 7,000/[1.05^6] = 5,223.51 euros.

Thus, 5,223.51 euros should be invested now to get 7,000 euros at the end of year 6 at 5% rate in interest, compounded annually.