Respuesta :
Answer: The total savings after four years will be £25,696.00, assuming interest is compounded annually.
We have
Annual Savings = £6,000
Interest rate per annum = 2.75%
No. of years = 4
Timing of savings = Beginning of the year.
Since the couple saves £6000 at the beginning of each year, we can treat this amount as an annuity due.
We assume that interest is compounded annually.
We use the following formula to arrive at the Future Value of an annuity due:
[tex] FVA = PV*\left [\frac{((1+r)^{n} -1)}{r} \right]*(1+r) [/tex]
Substituting the values in the equation above we get,
[tex] FVA = 6000*\left [\frac{(1+0.0275)^{4} -1)}{0.0275} \right]*(1+0.0275) [/tex]
[tex] FVA = 6000*\left [\frac{(1.114621259 -1)}{0.0275} \right]*(1.0275) [/tex]
[tex] FVA = 6000*\left [4.168045797]*(1.0275) [/tex]
[tex] FVA = 25696.00234 [/tex]
