MATH SOLVE

2 months ago

Q:
# Cynthia invests some money in a bank which pays 5% compound interest per year she wants it to be over 8000 at the end of three years what is the smallest amount to the nearest pound she can invest

Accepted Solution

A:

Answer:The smallest amount to the nearest pound she can invest is £6,911Step-by-step explanation:Letx -----> amount of money to be invested we know that The compound interest formula is equal to [tex]A=P(1+\frac{r}{n})^{nt}[/tex] where A is the Final Investment Value P is the Principal amount of money to be invested r is the rate of interest in decimal
t is Number of Time Periods n is the number of times interest is compounded per year
in this problem we have [tex]t=3\ years\\ P=x\\r=5\%=5\100=0.05\\n=1\\A>\£8,000[/tex] substitute in the formula above [tex]x(1+\frac{0.05}{1})^{1*3}> 8,000[/tex] [tex]x(1.05)^{3}> 8,000[/tex] [tex]x> 8,000/(1.05)^{3}[/tex] [tex]x> \£6,910.70[/tex] thereforeThe smallest amount to the nearest pound she can invest is £6,911