1.How much would be in your savings account in 11 years after depositing $150 today in the bank pays 8 percent per year? To 2dps.
Solution
Future value is the cash flows value in a period set at the future and is discounted at some estimated interest rate. The cash flows have a future value that is equal to the cash flows at the present period. The computations made are done as follow:
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FV N = PV (1+I) N
Here, PV is the present value, I stands for the interest rate, N is a compounding period and FV N stands for the future value.
Hence, the future value at 8% interest rate and cash as $150 is thereby computed as:
FV N = PV (1+I) N
= $150 (1+8%) 11
= $150 (1+0.08) 11
= $150 x 2.33164
= $349.746
= $349.75
Therefore, the amount at the interest rate 8% for 11 years is $349.75
2. Approximately how many years are needed to double a $100 investment when interest rates are 7 percent per year? To 2dps.
Solution
P(1+r) n = K, where K is the double investment of $200, n is the years with 7% on $100
Therefore, $100(1+7%) n = $200
$100(1+0.07) n = $200
Dividing both sides by $100,
(1+0.07) n = $200/$100 to get,
(1+0.07) n = 2
Hence, introducing logs on all sides:
n*log (1.07) = log 2
n=0.3010 / 0.0294
n= 10.238095238
Hence, the period is 10.24 years.
Alternatively, another way to tackle the question is making use of “Rule of 72”:
The period = $72 / 7 = 10.28571428571429
Period = 10.29 years for investment doubling.
3. What is the present value of a $350 payment in one year when the discount rate is 10 percent? To 2 dps.
Solution
PV = FV * [(1+(1+i) n )], where PV is the present value, FV is the payment/receiving amount in the future, n is the period number and i is the discount rate.
PV = $350 * [(1+(1+10%) 1 )],
PV = $350 * [(1+(1+0.1) 1 )],
PV = $350 * [(1+(1.1) 1 )],
PV = $350 * 0.909 PV factor table
PV = $318.15
Therefore, the above computation in obtaining $318.15 means that payment of $350 in a year with the discount rate at 10% is the same as the $318.15 now.
4. What is the present value of a $1,500 payment made in nine years when the discount rate is 8
percent? To 2 dps.
Solution
PV = $1,500 * [(1+(1+8%) 9 )],
PV = $1,500 * [(1+(1+0.08) 9 )],
PV = $1,500 * [(1+(1.08) 9 )],
PV = $1,500 * [1+1.9990], PV = $1,500 * 0.500 PV factor table
PV = $750
Therefore, the above computation in obtaining $750 means that $1,500 payment made in nine years with the discount rate at 10% is the same as the $750 now.
5. What is the future value of $500 deposited for one year earning an 8 percent interest rate annually? As a whole number.
Solution
FVN = PV (1+I) N where PV is the present value, FV is the payment/receiving amount in the future, n is the period number and i is the discount rate.
= $500 (1+8%) 1
= $500 (1+0.08) 1
= $500 x 1.08
= $540
Therefore, the amount at the interest rate 8% for 1 year is $540.
