(a) Themba wants to deposit a sum of money into a savings account so that he will have R30 000 in 3 years time for an overseas holiday how much money must he deposit into the account if the interest paid on the savings is 8,5% p.a (b) R1 000 is deposited in a savings account and two years later R2 000 is added to the savings.The interest is 5% p.a compounded annually calculate the amount of money accumulated in the account at the end of 5 years

Question

(a) Themba wants to deposit a sum of money into a savings account so that he will have R30 000 in 3 years time for an overseas holiday how much money must he deposit into the account if the interest paid on the savings is 8,5% p.a (b) R1 000 is deposited in a savings account and two years later R2 000 is added to the savings.The interest is 5% p.a compounded annually calculate the amount of money accumulated in the account at the end of 5 years

Answer 1

(a) To calculate the amount of money Themba must deposit into the savings account, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future amount (R30,000 in this case)
P = the principal amount (amount to be deposited)
r = annual interest rate (8.5% in this case)
n = number of times interest is compounded per year (assume it is compounded once per year)
t = number of years (3 years in this case)

By substituting the given values into the formula and solving for P, we can find the amount Themba needs to deposit:

R30,000 = P(1 + 0.085/1)^(1*3)

Simplifying the equation:

R30,000 = P(1.085)^3

Dividing both sides by (1.085)^3:

P = R30,000 / (1.085)^3

Using a calculator, compute (1.085)^3 to find its value, then divide R30,000 by that value. The result will be the amount of money Themba needs to deposit into the account.

(b) To calculate the amount of money accumulated in the account after 5 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future amount
P = the principal amount
r = annual interest rate (5% in this case)
n = number of times interest is compounded per year (assume it is compounded once per year)
t = number of years (5 years in this case)

Initially, R1,000 is deposited into the account, and after two years, an additional R2,000 is added. This means the principal amount after two years is R3,000.

Using the formula and substituting the values:
A = R3,000(1 + 0.05/1)^(1*3)

Simplifying the equation:
A = R3,000(1.05)^3

Inserting the values into the calculator, compute (1.05)^3 to find its value, then multiply R3,000 by that value. The result will be the accumulated amount in the account at the end of 5 years.