Walabuma deposits Br 550 a year for 10 years into his account that pays 8% compounded annually. After 10 years, Walabuma transfers the money into another account that pays 10% compounded quarterly. The money is left in the second account for 8 years.
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.
To solve this problem, we need to calculate the future value of the initial deposit in the first account after 10 years, and then calculate the future value of that amount after another 8 years in the second account.
For the first account, we'll use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where A is the future value, P is the principal amount, r is the annual interest rate in decimal form, n is the number of times the interest is compounded per year, and t is the number of years.
Using the given values:
P = 550 (the annual deposit)
r = 8% = 0.08 (the annual interest rate in decimal form)
n = 1 (compounded annually)
t = 10 (number of years)
Calculating the future value in the first account after 10 years:
A = 550 * (1 + 0.08/1)^(1*10)
A = 550 * (1 + 0.08)^10
A = 550 * (1.08)^10
A = 550 * 2.158927
A ≈ 1187.91
So, after 10 years, the amount in the first account would be approximately Br 1187.91.
Now, we need to calculate the future value of that amount in the second account after 8 years using the same formula:
P = 1187.91 (the amount transferred from the first account)
r = 10% = 0.10 (the annual interest rate in decimal form)
n = 4 (compounded quarterly)
t = 8 (number of years)
Calculating the future value in the second account after 8 years:
A = 1187.91 * (1 + 0.10/4)^(4*8)
A = 1187.91 * (1 + 0.025)^32
A = 1187.91 * (1.025)^32
A ≈ 1187.91 * 2.198218
A ≈ 2613.96
So, after 8 years in the second account, the amount would be approximately Br 2613.96.
Therefore, after 10 years in the first account and another 8 years in the second account, Walabuma would have approximately Br 2613.96.
To calculate the value of Walabuma's account after 10 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial principal (the amount Walabuma deposits each year)
r = the annual interest rate (8% in this case)
n = the number of times interest is compounded per year (annually in this case)
t = the number of years
Let's calculate the value of the account after 10 years:
P = 550
r = 8% or 0.08
n = 1 (compounded annually)
t = 10
A = 550(1 + 0.08/1)^(1*10)
A = 550(1 + 0.08)^(10)
A = 550(1.08)^10
A ≈ 1,369.86
So, after 10 years, the account has a value of approximately Br 1,369.86.
Now let's calculate the value of the account after 8 more years, when the money is transferred to another account that pays 10% compounded quarterly.
For compound interest calculated quarterly, we need to adjust the formula:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = initial principal
r = annual interest rate (10% in this case)
n = number of times interest is compounded per year (quarterly, so n = 4)
t = number of years (8 in this case)
Let's calculate the value of the account after 8 more years:
P = 1,369.86 (the value after 10 years)
r = 10% or 0.10
n = 4 (compounded quarterly)
t = 8
A = 1,369.86(1 + 0.10/4)^(4*8)
A ≈ 1,369.86(1 + 0.025)^(32)
A ≈ 1,369.86(1.025)^(32)
A ≈ 1,369.86(1.8173)
A ≈ 2,491.82
So, after 8 more years, the account has a value of approximately Br 2,491.82.