To calculate the final amount after 10 years of depositing money into the first account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case, Walabuma deposits Br 550 a year for 10 years into the account. The annual interest rate is 8%, compounded annually. We need to calculate the final amount after 10 years.
Using the formula:
A1 = P(1 + r/n)^(nt)
= 550(1 + 0.08/1)^(1*10)
= 550(1 + 0.08)^10
Calculating this expression will give us the final amount after 10 years in the first account.
After 10 years, Walabuma transfers the money into another account that pays 10% compounded quarterly. Now we need to calculate the final amount after 8 years in the second account.
A2 = P(1 + r/n)^(nt)
= A1(1 + r/n)^(n * 8)
= (previous amount)(1 + 0.10/4)^(4*8)
Calculating this expression will give us the final amount after 8 years in the second account.
Finally, to find the total amount at the end of the 10-year deposit and 8-year transfer period, you can add the amounts from the first and second accounts together.