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
To calculate the monthly deposit that Nadia needs to make to reach her goal of RM20,000 in 8 years, we can use the future value of an ordinary annuity formula. The formula is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value (RM20,000)
P = Monthly deposit
r = Interest rate per period (5%/12 = 0.00417)
n = Number of periods (8 years * 12 months/year = 96 months)
i. Now, let's calculate the monthly deposit (P):
20,000 = P * [(1 + 0.00417)^96 - 1] / 0.00417
To solve this equation, we can rearrange it to solve for P:
P = (20,000 * 0.00417) / [(1 + 0.00417)^96 - 1]
Calculating this, the monthly deposit P will be approximately RM180.45.
ii. Now, let's calculate the new monthly deposits required after the estimated cost of the wedding increased to RM30,000.
a) To find the new monthly deposit, we can use the same formula but with a future value of RM30,000:
30,000 = P * [(1 + 0.00417)^96 - 1] / 0.00417
Rearranging the equation to solve for P:
P = (30,000 * 0.00417) / [(1 + 0.00417)^96 - 1]
Calculating this, the new monthly deposit required would be approximately RM270.68.
b) If Nadia decides to make a lump sum deposit (X) at the end of two years instead of making additional monthly deposits, we can calculate the value of X using the future value of a single sum formula:
X = FV / (1 + r)^n
Where:
FV = Future value (RM30,000)
r = Interest rate per period (5%/12 = 0.00417)
n = Number of periods (8 years - 2 years = 6 years * 12 months/year = 72 months)
X = 30,000 / (1 + 0.00417)^72
Calculating this, the lump sum deposit required (X) would be approximately RM18,681.50.