NOTE: FV = future Value,
PV = Present Value
r = interest rate
n = time or years
P = principal
All values are in GHS
Q1.a. FV = p0 (1 + 𝑟)𝑛, = 1000 (1 + 0.04)20,
FV = 1000 (2.191) = 2192.12
Therefore, interest is equal to FV – Principal
Interest = 2191 – 1000 = 1191
b. Interest = p x r x t, annually interest = 1000 x 0.04 x 1 = 40
Total interest = 1000 x 0.04 x 20 = 800
C. The difference in answer a) and b) is that, in a) the interest component is reinvested with the
principal and accumulated to GHS 1191, while in b) the interest does not reinvest but only
accumulate to GHS 800.
Q2. FV = p0 (1 + 𝑟)𝑛 , 35 = 20(1+r)10
35
20
= (1+r)10 ; 1.75 = (1+r)10
√1.75
10
= 1 + 𝑟 ; 1.05755 = 1 + r
1.05755 – 1 = r;
r = 0.05755 or 5.75%
Q3. a) Number of years invested = 65 – 45 = 20
FVAN =
𝐏𝟎 [𝟏− (𝟏 + 𝐫 )𝐧]
𝐫
⟹
𝟏𝟓𝟎𝟎 [𝟏− (𝟏 +𝟎 .𝟏)𝟐𝟎]
𝟎.𝟏
; 1500(57.2749)
FVAN = 85912.35
b) Number of years invested = 70 – 45 = 25
FVAN =
𝟏𝟓𝟎𝟎 [𝟏− (𝟏 + 𝟎.𝟏 )𝟐𝟓]
𝟎.𝟏
; ⟹
𝟏𝟓𝟎𝟎 [𝟏− (𝟏 +𝟎 .𝟏)𝟐𝟎]
𝟎.𝟏
; 1500(98.347)
FVAN = 147520.58

c) FVAN =
𝐏𝟎 [𝟏− (𝟏 + 𝐫 )𝐧]
𝐫
⟹
𝟏𝟓𝟎𝟎 [𝟏− (𝟏 +𝟎 .𝟏)𝟐𝟎]
𝟎.𝟏
= 85912.35
If this continue to invest for additional five years, FV of 85912.35 = 85912.35 (1.1)5
Fv = 138362.69. The additional money will be 138362.69 – 85912.35 = 52450.34
9

Q15. Future value factor Annuity (FVan) =
𝐏𝟎 [𝟏− (𝟏 + 𝐫 )𝐧]
𝐫
Where po = present value,
r = rate of interest
n = number of years
For the investment of GHS 1000 each year for 10yeras
Fvan = [
1000 (1.1)10 −1
0.1
]
F Van = 1000 (15.937)
FVani = 15937.42
For the investment of GHS 2000 each year for 10yeras
Fvan = [
2000 (1.1)10 −1
0.1
]
FVan ii = 2000 (15.9374)
FVan = 31874.8
Total investment = 15937.42 + 31874.8 = 47812.22
Q16. Present value of Annuity = =
𝐏𝟎 [𝟏− ( 𝟏 + 𝐫 )−𝐧]
𝐫
PVan =
𝟏𝟎𝟎𝟎𝟎 [𝟏− ( 𝟏 .𝟎𝟖 )−𝟔]
𝟎.𝟎𝟖
+
𝟓𝟎𝟎𝟎 [𝟏− ( 𝟏 .𝟎𝟖 )−𝟔]
𝟎.𝟎𝟖
= 1000(4.622879) + 5000(4.622879)
PVan = 46228.79 + 23114.39 = 52246.34
Q17. Population growth at 5% = 5000 (1.05)10 + 5000 (1.05)15 + 5000 (1.05)20
= 8144 + 10395 + 13266
Per capita expenditure growth at 7% = 300 (1.07)10 + 300 (1.07)15 + 300 (1.07)20
= 590 + 828 + 1161

Total budget after 10, 15, and 20 years are (8144 x 590), (10395 x 828), (13266x 1161)
4804960, 8607060, 15401926
Q18. Alternative A. PVan =
𝐏𝟎 [𝟏− ( 𝟏 + 𝐫 )−𝐧]
𝐫
=
𝟐𝟕𝟓 [𝟏− ( 𝟏 .𝟏)−𝟓]
𝟎.𝟏
275 (3.791) = 1042.466
Alternative B.
𝟑𝟎𝟎 [𝟏− ( 𝟏 .𝟏 )−𝟐]
𝟎.𝟏
+
𝟐𝟓𝟎 [𝟏− ( 𝟏 .𝟏)−𝟐]
𝟎.𝟏
300 (1.7355) + 250 (2.0552)
520.65 + 513.82 = 1034.47
Q19. Loan amount is 150000, down payment is 50000, and balance is 100000
Annual Payment (PMT) in 20years at 8% =
𝑝𝑣
1−(𝟏 + 𝐫 )𝐧
𝑟
=
100000
1− ( 𝟏 .𝟎𝟖)−𝟐𝟎
.08
, =
100,000
9.8181
PMT = 10,185.23
For 25years at 9% PMT =
100000
1−( 𝟏 .𝟎𝟗)−𝟐𝟓
.09
= 100,000
9.8225
= 10180.62
At 25years, PMT = 10180.62.
The difference in the annual payment is 10185.23 – 10180.62 = 4.59
Q20. PV = 165000, PMT = 30000
PVan =
𝐏𝐌𝐓 [𝟏− ( 𝟏 + 𝐫 )−𝐧]
𝐫
, = 165000 =
𝟑𝟎𝟎𝟎𝟎[𝟏− ( 𝟏 .𝟎𝟔 )−𝐧]
.𝟎𝟔
165000
30000
=
1 – (1.06)−n
0.06
=
5.5 x .06 = 1 – (1.06)-n, = 0.33 = 1 – (1.06)-n
0.33 – 1 = - (1.06)-n , = 0.67 = - (1.06)-n
Log -0.67 = log – (1.06)-n =
Log −0.67
𝑙𝑜𝑔 −1.06
=
log – (1.06)−n
– (1.06)
−0.1739
0.0253
= -n, n = 6.87years