A person saves #30000 at 41/2% compound interest. She adds #8000 to her amount at the end of each year. Find her total savings after 2 years.
at time 0 30,000
at time 1 1.045*30,000+8,000
= 39,350
at time 2
1.045*39350 +8,000
= 49,120.75
Please I need the solving so that I will be able to understand the topic very well
To find the person's total savings after 2 years, we need to calculate the compound interest for each year.
First, let's find the amount of interest earned in the first year.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = final amount (including the principal and interest)
P = principal amount (the initial amount saved)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case:
P = #30000
r = 41/2% = 4.5% = 0.045 (convert to decimal)
n = 1 (interest is compounded once at the end of each year)
t = 1 (first year)
Now, we can calculate the amount of interest earned in the first year:
A1 = 30000 * (1 + 0.045/1)^(1*1)
A1 = 30000 * (1 + 0.045)^1
A1 = 30000 * (1.045)
A1 = #31350
After one year, the person's total savings, including the interest earned, is #31350.
Next, let's calculate the amount of interest earned in the second year.
Now, the principal amount is the previous total savings (#31350) plus the additional amount added at the end of each year (#8000).
P = #31350 + #8000 = #39350
r = 0.045 (as before)
t = 1 (second year)
A2 = 39350 * (1 + 0.045/1)^(1*1)
A2 = 39350 * (1 + 0.045)^1
A2 = 39350 * (1.045)
A2 = #41122.75
After two years, the person's total savings, including the interest earned, is #41122.75.
Therefore, the person's total savings after 2 years is #41122.75.