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2
2.1 Assume a firm makes a R3 500 deposit into its money market account. If this account is currently paying interest of 0,7%, what will the account balance be after one year? (2)
2.2 If David and July combine their savings of R4 250 and R1 750 respectively, and deposit this amount into an account that pays 6% annual interest, compounded monthly, what will the balance in the account be after four years? (2)
2.3 Joel just won R2,5 million in the lottery. She is given the option of receiving a total of R1,3 million now, or she can elect to be paid R100 000 at the end of every year for the next 25 years. If Joel can earn 5% annually on her investment, from a strict economic point of view, which option should she take? (5)
2.4 Joseph is a friend of yours. He has plenty of money but little finance sense. He received a considerable amount as a gift for his recent graduation and is looking for a bank in which to deposit the funds. HSBC Bank offers an account with an annual interest rate of 4% compounded monthly, while Dutch Bank offers an account with a 4,05% annual interest rate compounded quarterly. Recommend to Joseph which account he should choose. (3)
2.5 Gin and Tonic have just had their first child. If college is expected to cost R200 000 per year in 18 years, how much should the couple begin depositing annually at the end of every year to accumulate enough funds to pay the first year's tuition at the beginning of the 19th year? Assume that they can earn a 6% annual interest rate on their investment.
Expert Solution
2.1. Computation of Account Balance after one year:
Amount = Principal*(1+Rate)^Time
= 3,500*(1+0.7%)^1
Amount = 3,524.50
So, Account Balance after one year is R3,524.50
2.2. Computation of Account Balance after four year:
Amount = Principal*(1+Rate)^Time
= (4,250+1,750)*(1+6%/12)^(4*12)
= 6,000*1.27049
Amount = 7,622.93
So, Account Balance after four years is R7,622.93
2.3.
Option 1st: Receive R1.3 million now.
Computation of Future Value for Option 1st using FV Function in Excel:
=fv(rate,nper,pmt,-pv)
Here,
FV = Future Value = ?
Rate = 5%
Nper = 25 Years
PMT = 0
PV = R1,300,000
Substituting the values in formula:
=fv(5%,25,0,-1300000)
FV or Future Value = 4,402,261
Option 2nd: Receive R100 000 at the end of every year for the next 25 years.
Computation of Future Value for Option 2nd using FV Function in Excel:
=-fv(rate,nper,pmt,pv)
Here,
FV = Future Value = ?
Rate = 5%
Nper = 25 Years
PMT = R100,000
PV = 0
Substituting the values in formula:
=-fv(5%,25,100000,0)
FV or Future Value = 4,772,710
So, Option 2nd is better to choose.
2.4. Let us assume deposited amount $500,000
Option 1st : Compounded Monthly:
Computation of Future Value for Option 1st using FV Function in Excel:
=fv(rate,nper,pmt,-pv)
Here,
FV = Future Value = ?
Rate = 4%/12 = 0.33%
Nper = 12 months
PMT = 0
PV = $500,000
Substituting the values in formula:
=fv(0.33%,12,0,-500000)
FV or Future Value = $520,163.35
Option 2nd : Compounded Quarterly:
Computation of Future Value for Option 2nd using FV Function in Excel:
=fv(rate,nper,pmt,-pv)
Here,
FV = Future Value = ?
Rate = 4.05%/4 = 1.01%
Nper = 4 quarters
PMT = 0
PV = $500,000
Substituting the values in formula:
=fv(1.01%,4,0,-500000)
FV or Future Value = $520,559.63
As we can see that Future value is higher in case of Second option (Compounded quarterly). So, he should choose Dutch Bank offer.
2.5. Computation of Annual Deposit Amount using PMT Function in Excel:
=pmt(rate,nper,pv,-fv)
Here,
PMT = Annual Deposit Amount = ?
Rate = 6%
Nper = 18 Years
PV = 0
FV = 200,000
Substituting the values in formula:
=pmt(6%,18,0,-200000)
PMT or Annual Deposit Amount = 6,471.31
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