28.Nadia intends to get married in eight years time. She estimates that the cost of the wedding will be RM20000 then. She intends to save this amount by making equal monthly deposits at the end of each month in a bank that pays 5% compounded monthly
i.How much will this monthly deposit be?
ii.After paying for two years, that estimated cost of the wedding has gone up to RM30000
a)What should be the new monthly deposits?
b)In instead of making the additional monthly deposits, Nadia decides to make a lump sum deposit X at the end of two years, calculate the value of X
Can I know how to calculated (b)ii
As a start:
Because she is making regular deposits to save money, at the same frequency as compound interest is being accrued, this is a standard future value annuity. Use the future value annuity formula, taking care about which variable the question is asking you to find.
May I know how to find I
To find the monthly deposit amount that Nadia should make, we can use the formula for the future value of an annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = future value
P = monthly deposit
r = monthly interest rate
n = number of periods
In this case, Nadia wants to save RM20000 in 8 years, so the future value (FV) is RM20000. The interest rate (r) is 5% compounded monthly, which means the monthly interest rate is 5% / 12 = 0.4167%. The number of periods (n) is 8 * 12 = 96 months.
Substituting these values into the formula, we have:
20000 = P * ((1 + 0.004167)^96 - 1) / 0.004167
To solve for P, we can rearrange the equation:
P = 20000 * 0.004167 / ((1 + 0.004167)^96 - 1)
Calculating this using a calculator or a spreadsheet software, we find that the monthly deposit should be RM170.5694 (rounded to two decimal places).
i. Therefore, the monthly deposit Nadia needs to make is approximately RM170.57.
ii. After two years, the estimated cost of the wedding has increased to RM30000.
a) To find the new monthly deposits, we can use the same formula, but adjust the future value (FV) to RM30000:
30000 = P * ((1 + 0.004167)^96 - 1) / 0.004167
Solving for P, we find:
P = 30000 * 0.004167 / ((1 + 0.004167)^96 - 1)
Calculating this, we get that the new monthly deposit should be approximately RM255.70.
b) Instead of making additional monthly deposits, Nadia decides to make a lump sum deposit (X) at the end of two years. To calculate the value of X, we need to find the future value of the existing savings plus the lump sum deposit.
The future value of the existing savings after two years can be calculated using the formula:
FV = P * ((1 + r)^n - 1) / r
where P is the current monthly deposit, r is the monthly interest rate, and n is the number of periods (24 months in this case).
Using the current monthly deposit of RM170.57, the monthly interest rate of 0.4167%, and the number of periods as 24 months, we can find the future value of the existing savings.
FV = 170.57 * ((1 + 0.004167)^24 - 1) / 0.004167
Calculating this, we get that the future value of the existing savings is approximately RM4441.46.
To find the lump sum deposit (X) needed to reach the new target of RM30000, we subtract the future value of the existing savings from the new target:
X = 30000 - 4441.46
Therefore, the value of X is approximately RM25558.54.
ii. If Nadia decides to make a lump sum deposit instead of additional monthly deposits, the value of X should be approximately RM25558.54.