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Financial worksheet

Grade 11 to college · CCSS HSA.SSE.B.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Solve for: Number of periods (N)
- I/Y (annual interest rate): 9.5%
- PV (present value): 27,500
- PMT (payment each period): -425
- FV (future value): 0
- P/Y (payments per year): 10
- C/Y (compounding periods per year): 12
- Payments are made at the: End of each period (END)
Find: N (number of payments)
Answer
2.
Problem 2.
- Solve for: Payment (PMT)
- N (number of payments): 64
- I/Y (annual interest rate): 8%
- PV (present value): 30,000
- FV (future value): 0
- P/Y (payments per year): 11
- C/Y (compounding periods per year): 9
- Payments are made at the: End of each period (END)
Find: PMT
Answer
3.
Problem 3.
- Solve for: Present value (PV)
- N (number of payments): 50
- I/Y (annual interest rate): 8%
- PMT (payment each period): -600
- FV (future value): 0
- P/Y (payments per year): 16
- C/Y (compounding periods per year): 10
- Payments are made at the: End of each period (END)
Find: PV
Answer
4.
Problem 4.
- Solve for: Interest rate (I/Y)
- N (number of payments): 65
- PV (present value): 31,000
- PMT (payment each period): -400
- FV (future value): 0
- P/Y (payments per year): 13
- C/Y (compounding periods per year): 14
- Payments are made at the: Start of each period (BGN)
Find: I/Y (annual interest rate)
Answer
5.
Problem 5.
- Solve for: Future value (FV)
- N (number of payments): 50
- I/Y (annual interest rate): 4.8%
- PV (present value): 26,000
- PMT (payment each period): -450
- P/Y (payments per year): 15
- C/Y (compounding periods per year): 7
- Payments are made at the: Start of each period (BGN)
Find: FV
Answer
6.
Problem 6.
- Solve for: Future value (FV)
- N (number of payments): 55
- I/Y (annual interest rate): 7.7%
- PV (present value): 22,000
- PMT (payment each period): -600
- P/Y (payments per year): 12
- C/Y (compounding periods per year): 9
- Payments are made at the: Start of each period (BGN)
Find: FV
Answer
7.
Problem 7.
- Solve for: Interest rate (I/Y)
- N (number of payments): 38
- PV (present value): 18,000
- PMT (payment each period): -550
- FV (future value): 0
- P/Y (payments per year): 11
- C/Y (compounding periods per year): 13
- Payments are made at the: End of each period (END)
Find: I/Y (annual interest rate)
Answer
8.
Problem 8.
- Solve for: Number of periods (N)
- I/Y (annual interest rate): 5.5%
- PV (present value): 25,000
- PMT (payment each period): -500
- FV (future value): 0
- P/Y (payments per year): 9
- C/Y (compounding periods per year): 11
- Payments are made at the: Start of each period (BGN)
Find: N (number of payments)
Answer
9.
Problem 9.
- Solve for: Future value (FV)
- N (number of payments): 52
- I/Y (annual interest rate): 6.4%
- PV (present value): 22,500
- PMT (payment each period): -560
- P/Y (payments per year): 12
- C/Y (compounding periods per year): 11
- Payments are made at the: Start of each period (BGN)
Find: FV
Answer
10.
Problem 10.
- Solve for: Number of periods (N)
- I/Y (annual interest rate): 5.4%
- PV (present value): 24,000
- PMT (payment each period): -325
- FV (future value): 0
- P/Y (payments per year): 15
- C/Y (compounding periods per year): 14
- Payments are made at the: Start of each period (BGN)
Find: N (number of payments)
Answer

Answer key: Financial worksheet

1. N (number of payments): 100.9247
1. Give each amount a sign so the money balances: money you receive is positive, money you pay out is negative. Here PV (today's amount) = 27,500, PMT (each payment) = −425, FV (the amount at the end) = 0
2. Turn the yearly rate (I/Y) into the rate for one payment period (i), using 10 payments (P/Y) and 12 compounding periods (C/Y) a year
  $i = (1 + 9.5 ÷ 100 ÷ 12)^(12 ÷ 10) − 1$ $= 0.009507505$
3. Set up the one equation that ties all five keys together. N is the number of payments, and k = 0 because payments come at the end of each period (END)
  $PV·(1 + i)^N + PMT·(1 + i·k)·((1 + i)^N − 1) ÷ i + FV = 0$
4. Solve the equation for the missing N (ln is the natural logarithm): N = ln((PMT·(1 + i·k) − FV·i) ÷ (PMT·(1 + i·k) + PV·i)) ÷ ln(1 + i)
  $N$ $= 100.9247106066$
2. PMT: -587.84
1. Give each amount a sign so the money balances: money you receive is positive, money you pay out is negative. Here PV (today's amount) = 30,000, PMT (each payment) = −587.84, FV (the amount at the end) = 0
2. Turn the yearly rate (I/Y) into the rate for one payment period (i), using 11 payments (P/Y) and 9 compounding periods (C/Y) a year
  $i = (1 + 8 ÷ 100 ÷ 9)^(9 ÷ 11) − 1$ $= 0.0072668708$
3. Set up the one equation that ties all five keys together. N is the number of payments, and k = 0 because payments come at the end of each period (END)
  $PV·(1 + i)^N + PMT·(1 + i·k)·((1 + i)^N − 1) ÷ i + FV = 0$
4. Solve the equation for the missing PMT (g is short for (1 + i)^N): PMT = −(PV·g + FV) ÷ ((1 + i·k)·(g − 1) ÷ i)
  $PMT$ $= −587.8428369368$
3. PV: 26,490.49
1. Give each amount a sign so the money balances: money you receive is positive, money you pay out is negative. Here PV (today's amount) = 26,490.49, PMT (each payment) = −600, FV (the amount at the end) = 0
2. Turn the yearly rate (I/Y) into the rate for one payment period (i), using 16 payments (P/Y) and 10 compounding periods (C/Y) a year
  $i = (1 + 8 ÷ 100 ÷ 10)^(10 ÷ 16) − 1$ $= 0.0049925274$
3. Set up the one equation that ties all five keys together. N is the number of payments, and k = 0 because payments come at the end of each period (END)
  $PV·(1 + i)^N + PMT·(1 + i·k)·((1 + i)^N − 1) ÷ i + FV = 0$
4. Solve the equation for the missing PV (g is short for (1 + i)^N): PV = −(FV + PMT·(1 + i·k)·(g − 1) ÷ i) ÷ g
  $PV$ $= 26,490.4898746154$
4. I/Y (annual interest rate): -6.924701%
1. Give each amount a sign so the money balances: money you receive is positive, money you pay out is negative. Here PV (today's amount) = 31,000, PMT (each payment) = −400, FV (the amount at the end) = 0
2. Turn the yearly rate (I/Y) into the rate for one payment period (i), using 13 payments (P/Y) and 14 compounding periods (C/Y) a year
  $i = (1 + −6.9247007907 ÷ 100 ÷ 14)^(14 ÷ 13) − 1$ $= −0.005325678$
3. Set up the one equation that ties all five keys together. N is the number of payments, and k = 1 because payments come at the start of each period (BGN)
  $PV·(1 + i)^N + PMT·(1 + i·k)·((1 + i)^N − 1) ÷ i + FV = 0$
4. Solve the equation for the missing I/Y (g is short for (1 + i)^N): I/Y: the rate that makes PV·g + PMT·(1 + i·k)·(g − 1) ÷ i + FV = 0, found numerically
  $I/Y$ $= −6.9247007907$
5. FV: -6,062.58
1. Give each amount a sign so the money balances: money you receive is positive, money you pay out is negative. Here PV (today's amount) = 26,000, PMT (each payment) = −450, FV (the amount at the end) = −6,062.58
2. Turn the yearly rate (I/Y) into the rate for one payment period (i), using 15 payments (P/Y) and 7 compounding periods (C/Y) a year
  $i = (1 + 4.8 ÷ 100 ÷ 7)^(7 ÷ 15) − 1$ $= 0.003194169$
3. Set up the one equation that ties all five keys together. N is the number of payments, and k = 1 because payments come at the start of each period (BGN)
  $PV·(1 + i)^N + PMT·(1 + i·k)·((1 + i)^N − 1) ÷ i + FV = 0$
4. Solve the equation for the missing FV (g is short for (1 + i)^N): FV = −(PV·g + PMT·(1 + i·k)·(g − 1) ÷ i)
  $FV$ $= −6,062.5814372942$
6. FV: 8,404.44
1. Give each amount a sign so the money balances: money you receive is positive, money you pay out is negative. Here PV (today's amount) = 22,000, PMT (each payment) = −600, FV (the amount at the end) = 8,404.44
2. Turn the yearly rate (I/Y) into the rate for one payment period (i), using 12 payments (P/Y) and 9 compounding periods (C/Y) a year
  $i = (1 + 7.7 ÷ 100 ÷ 9)^(9 ÷ 12) − 1$ $= 0.0064098287$
3. Set up the one equation that ties all five keys together. N is the number of payments, and k = 1 because payments come at the start of each period (BGN)
  $PV·(1 + i)^N + PMT·(1 + i·k)·((1 + i)^N − 1) ÷ i + FV = 0$
4. Solve the equation for the missing FV (g is short for (1 + i)^N): FV = −(PV·g + PMT·(1 + i·k)·(g − 1) ÷ i)
  $FV$ $= 8,404.4391902432$
7. I/Y (annual interest rate): 8.664023%
1. Give each amount a sign so the money balances: money you receive is positive, money you pay out is negative. Here PV (today's amount) = 18,000, PMT (each payment) = −550, FV (the amount at the end) = 0
2. Turn the yearly rate (I/Y) into the rate for one payment period (i), using 11 payments (P/Y) and 13 compounding periods (C/Y) a year
  $i = (1 + 8.6640227226 ÷ 100 ÷ 13)^(13 ÷ 11) − 1$ $= 0.0078811478$
3. Set up the one equation that ties all five keys together. N is the number of payments, and k = 0 because payments come at the end of each period (END)
  $PV·(1 + i)^N + PMT·(1 + i·k)·((1 + i)^N − 1) ÷ i + FV = 0$
4. Solve the equation for the missing I/Y (g is short for (1 + i)^N): I/Y: the rate that makes PV·g + PMT·(1 + i·k)·(g − 1) ÷ i + FV = 0, found numerically
  $I/Y$ $= 8.6640227226$
8. N (number of payments): 59.4195
1. Give each amount a sign so the money balances: money you receive is positive, money you pay out is negative. Here PV (today's amount) = 25,000, PMT (each payment) = −500, FV (the amount at the end) = 0
2. Turn the yearly rate (I/Y) into the rate for one payment period (i), using 9 payments (P/Y) and 11 compounding periods (C/Y) a year
  $i = (1 + 5.5 ÷ 100 ÷ 11)^(11 ÷ 9) − 1$ $= 0.0061145018$
3. Set up the one equation that ties all five keys together. N is the number of payments, and k = 1 because payments come at the start of each period (BGN)
  $PV·(1 + i)^N + PMT·(1 + i·k)·((1 + i)^N − 1) ÷ i + FV = 0$
4. Solve the equation for the missing N (ln is the natural logarithm): N = ln((PMT·(1 + i·k) − FV·i) ÷ (PMT·(1 + i·k) + PV·i)) ÷ ln(1 + i)
  $N$ $= 59.4195484567$
9. FV: 3,966.53
1. Give each amount a sign so the money balances: money you receive is positive, money you pay out is negative. Here PV (today's amount) = 22,500, PMT (each payment) = −560, FV (the amount at the end) = 3,966.53
2. Turn the yearly rate (I/Y) into the rate for one payment period (i), using 12 payments (P/Y) and 11 compounding periods (C/Y) a year
  $i = (1 + 6.4 ÷ 100 ÷ 11)^(11 ÷ 12) − 1$ $= 0.0053320431$
3. Set up the one equation that ties all five keys together. N is the number of payments, and k = 1 because payments come at the start of each period (BGN)
  $PV·(1 + i)^N + PMT·(1 + i·k)·((1 + i)^N − 1) ÷ i + FV = 0$
4. Solve the equation for the missing FV (g is short for (1 + i)^N): FV = −(PV·g + PMT·(1 + i·k)·(g − 1) ÷ i)
  $FV$ $= 3,966.5293137972$
10. N (number of payments): 85.6349
1. Give each amount a sign so the money balances: money you receive is positive, money you pay out is negative. Here PV (today's amount) = 24,000, PMT (each payment) = −325, FV (the amount at the end) = 0
2. Turn the yearly rate (I/Y) into the rate for one payment period (i), using 15 payments (P/Y) and 14 compounding periods (C/Y) a year
  $i = (1 + 5.4 ÷ 100 ÷ 14)^(14 ÷ 15) − 1$ $= 0.0035995378$
3. Set up the one equation that ties all five keys together. N is the number of payments, and k = 1 because payments come at the start of each period (BGN)
  $PV·(1 + i)^N + PMT·(1 + i·k)·((1 + i)^N − 1) ÷ i + FV = 0$
4. Solve the equation for the missing N (ln is the natural logarithm): N = ln((PMT·(1 + i·k) − FV·i) ÷ (PMT·(1 + i·k) + PV·i)) ÷ ln(1 + i)
  $N$ $= 85.6348649519$