Marcus and Rachel want to save up $25 000 for a deposit on an apartment in 6 years' time. They aim to pay around half the deposit each. Marcus invests an inheritance of $9000 in a bank account where it earns 8% p.a. Rachel invests $100 at the beginning of each month where it earns 9% p.a.

a) What is the future value of Marcus's investment after 6 years? (Answer- 14 281.87)
b) How much will Rachel's investment be worth after 6 years? (Answer- $9571.96)

Thanks for any help

(a) 9000*1.08^6 = ?

(b) If the $100 had been invested at the end of each month, then the FV would have been
100((1+ .09/12)^72-1)/(1+.09/12 - 1) = 9500.71
Since it was invested at the beginning, it's like an extra month, but the original $100 has to be disregarded. So, the FV is
100((1+ .09/12)^73-1)/(1+.09/12 - 1) - 100
Study your formulas and their derivation.

Thank you. I read a) wrong. I did Q a) just like I did b). Didn't notice that a) was compound interest.

To calculate the future value of investments, we can use the compound interest formula:

Future Value = Principal * (1 + Interest Rate)^Time

a) To find the future value of Marcus's investment, we use the compound interest formula with a principal of $9000, an interest rate of 8% (expressed as 0.08), and a time of 6 years:

Future Value = $9000 * (1 + 0.08)^6
Future Value = $9000 * (1.08)^6
Future Value = $9000 * 1.593848
Future Value = $14,345.63

Therefore, the future value of Marcus's investment after 6 years is $14,345.63

b) To calculate Rachel's investment, we need to determine the future value of each monthly contribution and then sum them up.

First, we calculate the future value of each monthly contribution using the same compound interest formula but with a shorter time period of 6 years/12 months = 0.5 years for each monthly payment:

Future Value of each monthly contribution = Monthly Contribution * (1 + Interest Rate)^Time
Future Value of each monthly contribution= $100 * (1 + 0.09)^0.5
Future Value of each monthly contribution = $100 * (1.09)^0.5
Future Value of each monthly contribution = $104.9202

Next, we calculate the total future value by summing up the future value of each monthly contribution over the 6-year period:

Total Future Value = Future Value of each monthly contribution * Number of months
Total Future Value = $104.9202 * (12 months/year * 6 years)
Total Future Value = $104.9202 * 72
Total Future Value = $7,557.71

Therefore, the future value of Rachel's investment after 6 years is $7,557.71.