Loans and savings

An annuity loan has the same payment every period, a serial loan the same repayment. See the payment, the remaining debt and how much goes to interest — or find out how much to deposit to reach a savings goal.

The explanation is shown. Quick: amount, interest and years — monthly payment. Advanced: quarterly or yearly, outstanding balance, what another rate or term costs, and the table period by period.

Your numbers

What do you want to calculate?

Loan amount

Interest per year

Your own interest rate — from the loan offer, the bank or the exercise.

Term

More options: how often you pay, Remaining debt after period, Table

You pay

Remaining debt after period no.

Show table for

Answer

Payment per month (annuity loan)

2,121.31DKK

Remaining debt after 12 periods

184,185.12DKK

Total interest, annuity loan

54,557.24DKK

Serial loan: first and last payment

2,500.00 → 1,673.61DKK

Total interest, serial loan

50,416.67DKK

Total paid, annuity loan

254,557.24DKK

Effective annual rate

5.116%

How to work it out

1r = 5 % / 12 = 0.4167 % · n = 10 · 12 = 120The rate and the number of periods must match: monthly payments mean a monthly rate and a number of months.
2y = 200,000 · 0.004167 / (1 − (1 + 0.004167)^−120) = 2,121.31The annuity formula finds the payment that covers both interest and the whole loan over n periods.
3First period: interest 833.33 + repayment 1,287.98 = 2,121.31At the start the debt is large, so most of the payment is interest. The repayment grows each period.
4Remaining debt after 12 periods: DKK 184,185.12The remaining debt is the loan with interest minus the payments with interest, up to period k.
5Serial loan: repayment = 200,000 / 120 = 1,666.67 per monthThe serial loan repays the same amount each time, so the payment falls as the interest falls.
6Total interest: annuity 54,557.24 · series 50,416.67The serial loan pays the debt down faster and therefore costs less in interest — but the payment is largest at the start.

The formula

y = H · r / (1 − (1 + r)⁻ⁿ)

Annuity loan: the same payment y every period. H is the loan amount, r the rate per period, n the number of periods.

balance = H · (1 + r)ᵏ − y · ((1 + r)ᵏ − 1) / r

The remaining debt after k periods.

repayment = H / n · interest = balance · r

Serial loan: the same repayment every period, so the payment falls.

y = (goal − K₀ · (1 + r)ⁿ) · r / ((1 + r)ⁿ − 1)

Savings: the deposit per period that reaches the goal.

Fees, contributions and price losses are not included. They are in the loan offer and make the loan more expensive than the interest alone.

Keep calculating

Calculators from the education programmes that work out the same topic in more detail.

Annuity loan – repayment
What will the monthly payment on an annuity loan be?
Serial loan – repayment and outstanding debt
How does the payment on a serial loan develop, and what does it cost in total interest?
APR / effective annual interest rate
What is the effective annual rate when interest is added several times a year?
Overdraft facility – interest cost
What does it cost to draw a certain amount on the overdraft for a number of days?
Late payment interest
How much late-payment interest does the debtor owe when an invoice is paid late?

In depth: more numbers and “what if”

What if the interest rate is different?

Interest per year	Payment per month	Total interest
4 %	2,024.90 DKK	42,988.33 DKK
4.5 %	2,072.77 DKK	48,732.18 DKK
5 %	2,121.31 DKK	54,557.24 DKK
5.5 %	2,170.53 DKK	60,463.07 DKK
6 %	2,220.41 DKK	66,449.20 DKK

What if the term is different?

Term	Payment per month	Total interest
5 year	3,774.25 DKK	26,454.80 DKK
10 year	2,121.31 DKK	54,557.24 DKK
20 year	1,319.91 DKK	116,778.75 DKK
30 year	1,073.64 DKK	186,511.57 DKK

Annuity loan period by period

Period	Capacity	Interest	Repayment	Remaining debt
1	2,121.31	833.33	1,287.98	198,712.02
2	2,121.31	827.97	1,293.34	197,418.68
3	2,121.31	822.58	1,298.73	196,119.95
4	2,121.31	817.17	1,304.14	194,815.80
5	2,121.31	811.73	1,309.58	193,506.23
6	2,121.31	806.28	1,315.03	192,191.19
7	2,121.31	800.80	1,320.51	190,870.68
8	2,121.31	795.29	1,326.02	189,544.66
9	2,121.31	789.77	1,331.54	188,213.12
10	2,121.31	784.22	1,337.09	186,876.03
11	2,121.31	778.65	1,342.66	185,533.37
12	2,121.31	773.06	1,348.25	184,185.12
13	2,121.31	767.44	1,353.87	182,831.24
14	2,121.31	761.80	1,359.51	181,471.73
15	2,121.31	756.13	1,365.18	180,106.55
16	2,121.31	750.44	1,370.87	178,735.69
17	2,121.31	744.73	1,376.58	177,359.11
18	2,121.31	739.00	1,382.31	175,976.79
19	2,121.31	733.24	1,388.07	174,588.72
20	2,121.31	727.45	1,393.86	173,194.86
21	2,121.31	721.65	1,399.67	171,795.20
22	2,121.31	715.81	1,405.50	170,389.70
23	2,121.31	709.96	1,411.35	168,978.35
24	2,121.31	704.08	1,417.23	167,561.11
25	2,121.31	698.17	1,423.14	166,137.98
26	2,121.31	692.24	1,429.07	164,708.91
27	2,121.31	686.29	1,435.02	163,273.88
28	2,121.31	680.31	1,441.00	161,832.88
29	2,121.31	674.30	1,447.01	160,385.87
30	2,121.31	668.27	1,453.04	158,932.84
31	2,121.31	662.22	1,459.09	157,473.75
32	2,121.31	656.14	1,465.17	156,008.58
33	2,121.31	650.04	1,471.27	154,537.30
34	2,121.31	643.91	1,477.40	153,059.90
35	2,121.31	637.75	1,483.56	151,576.34
36	2,121.31	631.57	1,489.74	150,086.60
37	2,121.31	625.36	1,495.95	148,590.65
38	2,121.31	619.13	1,502.18	147,088.46
39	2,121.31	612.87	1,508.44	145,580.02
40	2,121.31	606.58	1,514.73	144,065.30
41	2,121.31	600.27	1,521.04	142,544.26
42	2,121.31	593.93	1,527.38	141,016.88
43	2,121.31	587.57	1,533.74	139,483.14
44	2,121.31	581.18	1,540.13	137,943.01
45	2,121.31	574.76	1,546.55	136,396.46
46	2,121.31	568.32	1,552.99	134,843.47
47	2,121.31	561.85	1,559.46	133,284.01
48	2,121.31	555.35	1,565.96	131,718.05
49	2,121.31	548.83	1,572.49	130,145.56
50	2,121.31	542.27	1,579.04	128,566.53
51	2,121.31	535.69	1,585.62	126,980.91
52	2,121.31	529.09	1,592.22	125,388.69
53	2,121.31	522.45	1,598.86	123,789.83
54	2,121.31	515.79	1,605.52	122,184.31
55	2,121.31	509.10	1,612.21	120,572.10
56	2,121.31	502.38	1,618.93	118,953.17
57	2,121.31	495.64	1,625.67	117,327.50
58	2,121.31	488.86	1,632.45	115,695.06
59	2,121.31	482.06	1,639.25	114,055.81
60	2,121.31	475.23	1,646.08	112,409.73
61	2,121.31	468.37	1,652.94	110,756.79
62	2,121.31	461.49	1,659.82	109,096.97
63	2,121.31	454.57	1,666.74	107,430.23
64	2,121.31	447.63	1,673.68	105,756.55
65	2,121.31	440.65	1,680.66	104,075.89
66	2,121.31	433.65	1,687.66	102,388.23
67	2,121.31	426.62	1,694.69	100,693.54
68	2,121.31	419.56	1,701.75	98,991.78
69	2,121.31	412.47	1,708.84	97,282.94
70	2,121.31	405.35	1,715.96	95,566.97
71	2,121.31	398.20	1,723.11	93,843.86
72	2,121.31	391.02	1,730.29	92,113.56
73	2,121.31	383.81	1,737.50	90,376.06
74	2,121.31	376.57	1,744.74	88,631.32
75	2,121.31	369.30	1,752.01	86,879.30
76	2,121.31	362.00	1,759.31	85,119.99
77	2,121.31	354.67	1,766.64	83,353.35
78	2,121.31	347.31	1,774.00	81,579.34
79	2,121.31	339.91	1,781.40	79,797.95
80	2,121.31	332.49	1,788.82	78,009.13
81	2,121.31	325.04	1,796.27	76,212.85
82	2,121.31	317.55	1,803.76	74,409.10
83	2,121.31	310.04	1,811.27	72,597.83
84	2,121.31	302.49	1,818.82	70,779.01
85	2,121.31	294.91	1,826.40	68,952.61
86	2,121.31	287.30	1,834.01	67,118.60
87	2,121.31	279.66	1,841.65	65,276.95
88	2,121.31	271.99	1,849.32	63,427.63
89	2,121.31	264.28	1,857.03	61,570.60
90	2,121.31	256.54	1,864.77	59,705.83
91	2,121.31	248.77	1,872.54	57,833.30
92	2,121.31	240.97	1,880.34	55,952.96
93	2,121.31	233.14	1,888.17	54,064.79
94	2,121.31	225.27	1,896.04	52,168.75
95	2,121.31	217.37	1,903.94	50,264.81
96	2,121.31	209.44	1,911.87	48,352.93
97	2,121.31	201.47	1,919.84	46,433.09
98	2,121.31	193.47	1,927.84	44,505.25
99	2,121.31	185.44	1,935.87	42,569.38
100	2,121.31	177.37	1,943.94	40,625.44
101	2,121.31	169.27	1,952.04	38,673.41
102	2,121.31	161.14	1,960.17	36,713.23
103	2,121.31	152.97	1,968.34	34,744.90
104	2,121.31	144.77	1,976.54	32,768.36
105	2,121.31	136.53	1,984.78	30,783.58
106	2,121.31	128.26	1,993.05	28,790.54
107	2,121.31	119.96	2,001.35	26,789.19
108	2,121.31	111.62	2,009.69	24,779.50
109	2,121.31	103.25	2,018.06	22,761.43
110	2,121.31	94.84	2,026.47	20,734.96
111	2,121.31	86.40	2,034.91	18,700.05
112	2,121.31	77.92	2,043.39	16,656.66
113	2,121.31	69.40	2,051.91	14,604.75
114	2,121.31	60.85	2,060.46	12,544.29
115	2,121.31	52.27	2,069.04	10,475.25
116	2,121.31	43.65	2,077.66	8,397.58
117	2,121.31	34.99	2,086.32	6,311.26
118	2,121.31	26.30	2,095.01	4,216.25
119	2,121.31	17.57	2,103.74	2,112.51
120	2,121.31	8.80	2,112.51	0.00

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