Question

Dan invests £2200 into a savings account. The bank gives 5% compound interest for the first 3 years and 4% thereafter. How much will Dan have after 7 years to the nearest pound?

Answer 1

Present value = 2200
interest rates =5% for 3 years, and 4% afterwards
no. of periods = 7

Future value=2200*(1.05)^3(1.04)^(7-3)
=£2979.367   (please round to appropriate number of decimals)

Answer 2

The correct answer, to the nearest pound, is:

2979

Explanation:

Compound interest can be written as an equation of the form

$y=a(1+r)^t$,

where a is the initial deposit, r is the interest rate as a decimal number, and t is the number of years.

For the first 3 years, we have a = 2200, r = 5% = 5/100 = 0.05; and t = 3:

$y=2200(1+0.05)^3\\\\=2200(1.05)^3=2546.775$

This will be the "initial deposit" in the account with 4% interest.  This gives us that

a = 2546.775; r = 4% = 4/100 = 0.04; and t = 7-3 = 4:

$y=2546.775(1+0.04)^4\\\\=2546.775(1.04)^4=2979.367 \approx 2979$