Financial Maths Question

bluesnow

Dermot has 5000 euro and would like to invest it for two years. A special savings account is offering a rate of 3% for the first year and a higher rate for the second year, if the money is retained in the account. Tax of 41% will be deducted each year from the interest earned.

(a) How much will the investment be worth at the end of one year, after tax is deducted?

(b) Dermot calculates that, after tax has been deducted, his investment will be worth 5223.60 euro at the end of the second year. Calculate the rate of interest for the second year. Give your answer as a percentage, correct to one decimal place.

Help please!

dlouth15

How to do part a)

1. Multiply the principle, 5000, by 3% (i.e. 3/100) to get the interest on the first year.
2. Multiply this interest figure by 41% (i.e. 41/100) to get the tax on the first year.
3. Add the interest figure and subtract the tax figure from the principle.

Part b involves solving an equation.

We've worked out the that at the start of the second year we have an amount, call it P. This P is then multiplied by a new rate, R, to give a new interest I. Tax of at a rate 41% is then applied to I to give the total tax deduction, I. The final figure 5223.6 is then equal to P + I - T.

So we have I = P * R, T=P*R*0.41

And so 5223.6 = P + I - T
= P + P*R - P*R*0.41
Simplifying
5223.6 = P(1 + R - R*0.41)
= P(1 + R(1-0.41)
= P+0.59PR

Rearranging
0.59PR= 5223.6 - P

Therefore
R = (5223.6 - P) / (0.59P)

We know P from the answer to the first part, so we now know R, the answer to the second part. Don't forget to multiply R by 100 to express the rate as a percentage.